EP 400 Building a Recurring Revenue Model: Key Insights

The Pest Management space um and you become a really big player in The Pest Management space. Uh that’s a win, but then maybe you unlock some other verticals as well, and then you become that home run. But at the least you hit that double right, and I think, like one of the things to your thing about red flags, is like Founders. Have this Vision, this Grand Vision, which is awesome but like what are the ACT yeah? What’s the tangible? steps? Hey welcome back to the program, and today we are so blessed to have with us Adam, and I love, I love what Adam does so.

This is going to be a really fun interview. Adam. Will you tell us who you are and what you do? Yeah absolutely thanks for having me Todd. Of course my name is Adam C. I am one of the co-founders and the chief marketing officer of a company called Yorkie uh. We are a strategic growth and investment firm, which uh really just means that we try to help technology companies grow. We do that through two different ways. One is on the investment side of uh, where we invest in early stage.

B2B software recurring Revenue companies uh, and then we have an advisory Services side of the business where we help companies with both strategy and operational execution in finance, product marketing and sales love it and so primarily you’re dealing with SAS companies right and the technology with monthly Recurring, that’s kind of another way for saying SAS right or is it? Is it different? Okay? Okay?

So so, as you jump into the SAS World, obviously there’s a lot of players here and there’s a lot of people that need to hear this interview, I’m guessing because it’s it there’s a lot of ways to screw it up, and so everyone thinks that jumping into A recurring Revenue model is easy. Tell us what you see, what are, as you are, trying to um well, first of all tell us why. Why are you into this Marketplace?

Have you had something like this before personally, or what kind of drove you into this uh, this advisory, this type Ty advisory, yeah, absolutely so uh prior to um, starting York, IE uh, I worked with my two partners at a company called dine, which did the domain Name system, so very deep technical infrastructure, um and we really uh were – were sort of the go to Market side of that business that we were able to grow to about a 100 million annual recurring revenue and washed by Oracle.

Nice and as we reflected back on that growth Journey uh, and we looked at all of the different sort of um Legacy institutions that we turn to help, whether that was our VC, whether that was our vendors, whether that was our advisers, we kind of felt like They were operating out of antiquated models, uh right that were beneficial to them, but not necessarily to us as The Operators right, and so we wanted to disrupt that, and so that was the Genesis for launching York IE, because to your point, B2B software is very Competitive, but it’s also still at its infancy right and so I think, a lot of opportunity for companies to continue to grow, but uh continue to grow.

One of the things that we’ve always advocated, for which is, I think, because we’re based in New Hampshire, is uh – is strategic, efficient growth, not necessarily growth at all costs nice, nice.

That’s a Viewpoint. We’ve been trying to bring to the market. I think that’s a good. I think that’s a good Viewpoint to bring to the market, I think there’s a lot of people that just grow to grow and sometimes you’re like what are you doing playing in this in this uh part of the niche? You know what I mean. It’s kind of goofy simp s, so absolutely now you were very casual in saying that you reached 100 million in recurring annual revenue.

That is no small feat. Congratulations by the way it’s awesome, yeah, thank you and for those of you listening who are trying to build a recurring monthly Revenue model. There are a lot of things to consider in building. You know, there’s so many different facets of of SAS and there’s. So many different ways to hit this Adam when you’re evaluating opportunities for your investment site or your advisory. What are some red flags? You see, I mean there’s. Obviously, things people do wrong and everyone thinks that everything goes right in SAS.

What are some red flags that you see that you’re like yeah, this probably isn’t going to work for us, I mean, I think, one of the things that you see a lot of ums is sort of like a product out approach. Okay, right, like a lot of times like especially for new companies, you’ll, have some sort of a Founder. That’s a subject matter expert in a field and had a problem, so they solved it so now they assume everybody else, wants it as well too got and what we always advocate for is a market in approach right, which is like okay, great, like that’s awesome.

What you know your product, but how does your product play in the broader competitive landscape? Because right successful companies have not just featured for features sake, but they have featured that people want and they are. They are rising as the market is expanding um and I think, taking that kind of in approach and as early as possible will help influence sort of everything that you build. Uh for your. So, are you talking more about just really paying attention to what your competitors are doing or paying more attention to what your current subscribers are saying?

They want, I think, the combination of all of those things I think you’re right too I just I was wondering I don’t. I don’t look at as many use cases as you do, so I’m really, I’m really actually very curious about this, because so many people out there, especially Developers, are trying to create something. That’s going to build that monthly recurring. Everyone wants monthly, recurring or annual recurring, and so as you’re looking at that and trying to build that what are some of the big green lights, I mean you probably look out on the landscape of the opportunities that you see and you’re like dude.

I wish I had a piece of that one you know well, are there? Are there things and opportunities you see that that uh that are really just like you know, they’re going to work. I think what I, what I am, and the company is really big into – is like at this moment like a vertical SAS that has horizontal applications.

Okay, because like to our point about the pragmatic growth right, like you know, the old Silicon Valley model is like a home run or I strike out right, I’m much more of like a Moneyball approach. Right like hey, can you manufacture a double and then, like? Hey, if that’s where you end up like you know, if you have a a platform that uh and kind of attacking say like the The Pest Management space um and you become a really big player in The Pest Management space. Uh, that’s a win. But then maybe you unlock some other verticals as well, and then you become that home run, but at the least You’ hit that double right, and I think, like one of the things to your thing about red flags, is like Founders.

Have this Vision, this Grand Vision, which is awesome but like what are everybody? Wants it yeah. What’s the tangible steps to get there yeah right and that’s what I like that the unlock additional opportunity as you go along, I like it, I like it now Adam one of the things that makes you unique in term from an investment standpoint is that you Do have this advisory side to you. You know. I think that a lot of people out there listening who are attempting to raise their initial seed rounds or maybe you’re in an A or B round a lot of people. They look for the wrong things.

They don’t really know what this this investor is looking at when they’re looking at their financials looking at their numbers looking at their product even and you have the unique advantage of being able to come in and not only offer the funds that they need, but Also the advisory piece: how important is it for people to be looking for a strategic money as opposed to just any money to help fund their business yeah? I mean, I think, that’s like going back to the to the point you made about like having just seen.

Companies like raising a bunch of capital, it’s like you, have to understand, uh that you know what I mean that is like you are selling a piece of your company when you raise money and yeah, just as just as you are so thoughtful uh in who you Co-Found it with and who you bring in as a leadership team. The same should be said about who you bring in as an investor right and not all money is created equal, and so you want to find a partner who’s, bringing some additional value and also viewing the opportunity in the same way that you do, because when there’s Misaligned expectations and misaligned incent.

It really takes the joy out of the startup Journey, which is going to be hard even on its best day and like loses sort of the whole point of it. If it’s just not a great experience now I know that in talking with a lot of other, you know, different Industries have different exit strategies right um.

You know there’s a lot of service providers who really don’t see an exit until it’s time to retire, and they just want to exit to maybe family or pass it on. You know through that kind of exit strategy, which is a strategy, but when it comes to SAS, there’s tends to be this. Mindset of all I got to do is hit this Revenue number and then I should get this multiple. What else is there to it?

Because a lot of guys, you know they tend to think that they overstimulate what their perceived valuation of the company is. How do you look at valuation? You know a lot of these guys are just kind of bloated in their own heads yeah.

I mean, I think last couple of years in Tech have been a reckoning of that uh, false valuations, as it turns out that, like a three million revenue, company is not worth a is not valued at two billion dollars, surprising everybody um, but that’s Where again, I think it’s about you know.

I have always believed good companies have good options and if you take that look at the beginning – and you take that market in approach – and you have a full understanding of what kind of company you’re trying to build and then you go about build it in a Responsible manner, you have a lot of options right. My co-founder and my longtime friend Kyle York, his most retweeted tweet is saying.

Like you know, in the tech industry we have to celebrate a $ 25 million exit because that’s still right for the founder and the founder that game changer, yeah exactly right but like in the tech crunch world and you know the Sequoia world, like those Are like scoffed at really. I know crazy right. It’S crazy! There’s a lot more of a universe, uh of potential opportunities for that than the uh you know3 billion uh exits just a few seconds to let you know about a project that we’ve been putting together for the last several months and we’re finally launching it called the Captain’s Council, you see as a CEO or operator of a business, it can feel like you get stuck in your own head, a lot of the time you get challenges that you don’t know how to resolve.

You get people causing problems in your leadership team that you don’t know how to resolve, and it’s so hard to overcome those things by yourself. You don’t have to anymore join the Captain’s Council. Captain’s Council is a group of other CEOs and operators and owners of businesses where we come together once a month for several hours to discuss the biggest challenges, you’re facing you express to the council 8 to 10 people about what’s going on. Where do you feel stuck, and these other people are in the same boat as you, they’re running and operating their own businesses they’re your peers?

They help you kind of dissect what’s happening and help. You see things that you may not have seen all by yourself. If you don’t have a good strong network of people around, you come join the Captain’s Council. This is going to be something that will change the way. You run your business and open your eyes to opportunities that you have never seen without the help of your peer group. Come check it out.

Captain council.com, you know which, which leads to another question. You know that there are not all founders created equal. I think you’d agree with me there um and, as you think, about Founders in Tech, some people are clearly very, very Advanced and Technical in terms of their ability to visualize a platform that can solve a lot of really cool problems and then there’s others that are Just really good at being the face of the company and and the Visionary and and kind of guiding it that way. As you look at both types of leaders in these SAS companies, you know clearly, there just are points where certain people are meant to exit.

Sooner than others, where do you see that difference in in those two different personality types that we just talked about yeah?

It’s interesting and I think that that that realization, that not every company and not every stage is right for every person is a very liberating right thing right and that’s where, like I love working with second time entrepreneurs, because they kind of understand that a little Bit a first-time entrepreneur, even myself, as a first-time co-founder right, like it’s very easy to fall into the um. Oh, I must be doing something wrong, because this part of what used to be my kingdom is now moving to somebody else, and the reality is You’ actually done something right, like a lot of times.

In those early days like um, you have kind of two jobs because there’s not enough, you know, and then it’s like well, if you’ve done your job, two or 10 yeah right, yeah, yeah, exactly right, um, and so you know what I mean, and I think That, like you know, I talked with a performance coach once and she said you know. Most companies fail not because of external factors, but because of internal factors, agree right and I think just having that self-awareness um can be the difference for different Founders on their on the different stops on their journey love. It loves it now.

Let’s take a step back now that we know kind of who you’re trying to help how you help them the problems you’re trying to solve. Let’s talk a little bit about your business, I mean you guys have been doing this now for how long, so we founded the company uh in September of 2019, so we’re going on four years. Oh just right before right as people were starting to get that that cold right, it was very yeah thought, and it’s funny that you say that, because we thought like okay, we wanted to have this sort of Hands-On investment approach, so we thought very biased to the Northeast being in New Hampshire and then then the world shut down um and it didn’t matter if you were in the town next to me or if you were in Utah right um, which really expanded our model and opportunity.

Because I truly believe there are great entrepreneurs everywhere, and I really do think that we are entering into the sort of phase where, like you know, the Silicon valleys of the world and the Austin and the New Yorks that they aren’t goon na. Have that strangle. Hold – and I I agree with you yeah, you know, and it’s smart, I agree with you and that’s a fun opportunity to try to go and look and find those uh, those Founders doing cool things. I love it. I love it.

You know I agree with you in a lot of ways and I’m glad that you had a positive effect from covid, because it does it did. It did really really launch people out of their own Comfort zones in a lot of ways and um. So so, as you started to like, you know, build this model which came first, the advisory or the investment. What kind of LED, which came?

First, in your little puzzle, there uh the investment side came first because, as it turns out easier, it’s easier to give money uh than to ask and then right what we did was we kind of piloted that Hands-On uh execution with the companies that we were investing In and then we found that there was real product Market fit and there was that real need um at that sort of C early CA, and then we were able to then go and say: okay great now, let’s go take that to more companies, and then I love it as a result. That’s continued to grow and um and be, but you knew from the start that companies you wanted to invest in. You wanted to help guide and Coach is.

That is that right? You wanted to strategically kind of align with companies that you knew how to expand and grow. Is that right to your to your point about what kind of capital did we want to be right? Like yeah, I a lot of traditional VCSS are more money managers um, who think that companies are built in spreadsheets, whereas I think we realize that companies are built by human beings, and we want to get involved with those human beings and help them. You know chase their dreams. I love that.

You say that because I have, I am a self-proclaimed Master at playing spreadsheet, billionaire and um, and it does definitely take a real executioner, though, to really take the model and put it into action. And I think to your point: it’s a beautiful thing that you’re doing you know you’re, really kind of helping them understand the spreadsheet that they’ve put together to pitch you with and now say, okay to really execute on this. You don’t just need the money you need X, Y and Z. Also, how do you fulfill that with these guys yeah?

So, we’ve built a very large like a very strong um, uh Team, so across those services that I talked about, we have over about 120 employees. Love – and I always joke with my co-founders that we had to start the company because right now we’re not even qualified for an internship, because we’ve been able to attract such talented folks um, because I think they believe in our in our vision of you know really Helping reshape the way startups are built, scaled and monetized. I love it.

I love it and, as you as you jump in um, you know after Investments have been made and you really jump into to more of the advisory and plugging people in what does that? Look? Like are you? Are you replacing people? Are you just supplementing like? Are you coaching training? What are the typical problems?

You’re, seeing on initial early stage, guys yeah, absolutely and just to clarify the point too, like we’re doing these advisory services for both the companies that we invest in and just companies in general? What we’re seeing is like a lot of companies will come to us with a point solution like hey. We just had the seed funding, we want to do an announcement and we want to start building our brand um yeah. In that case, we’ll come in. We have like a basically like your Swiss army knife of a marketing team. We can either directly Co.

You know work with the co-founder or potentially maybe you have a a more Junior marketing resource that you want to right, and so that’s those are the problems we’re seeing hey. We got some funding uh, we need to accelerate the product, we need some Dev help. Um love it hey, we have the we have the product, we want to go and build, build a brand and tell a story or hey. We have some traction now, but like is our sales process as clean as it could be? You know we’re not really, we’re on a spreadsheet, not a CRM, and we come in and help them in all those different areas. I love it. What a fun stage and you’re really attracting, I think the types of people listening to this podcast and so for those of you listening.

I hope, you’re really listening carefully, because a lot of you are at that stage where you’re launching or launched, and now that you’ve launched you kind of look around. You say: okay, we’re making money. Um we’ve got revenue coming in, we’ve got great team.

What do we do next, and – and so I love people like you, who can actually jump in and say, Here’s the strategy, here’s what needs to happens next, but let’s evaluate where you’re at right now that that kind of, where you’re at in a lot of ways, Yeah absolutely and that’s where we’d have like a lot of times, we’ll start with, like a kind of like a corporate strategy, Deep dive project that we work with companies right, look at the financial model. We look at this. You know the the tech stack. We look at the website architecture and we just come in and help make suggestions about. You know love it up.

You know this is this. Is such a great conversation to have you know and as you do this and as you’ve been able to grow to these hund and whatever Plus employees and this team that you’re building?

How, where do you anticipate taking it, I mean? What’s your strategy, do you have an exit plan or is this kind of a forever grow and skill game that you’re playing yeah, I mean like uh, you know. I always say that I started working in York ice in kindergarten, because that’s when I met my partner Cloud York for the first time um, and so we really do want too yeah. We want to build something of uh of substance and in scale, and so I think, two areas that we’re doing that is like we’re continuing on our full-service business.

But one of the things that we realized was that companies even earlier in the journey right at that ideation stage um. They have all the same problems, but they have even less done to solve them, and so we’re really trying to productize our full service into a sort of a strategic growth platform that um earlier stage. Entrepreneurs can selfservice thems on and and get more value and uh. You might see. I have like a little stat up here. That says, 80 % of startups fail, and I believe that a lot of that is at those earliest days where they just don’t to our point about hey. These companies are growing everywhere.

They may not have access to some of that strategic advice. They might not have access to some of those resources, so if we can figure out a way to get them some of that stuff even earlier, maybe that number goes down to 75 % or 70 % and then you’re talking about millions of people that are being Able to fulfill their dreams, which to us is a really exciting problem to tackle.

I love it love it. Yeah, there’s, definitely no shortage of people that need the things you’re, giving yes right and that’s it like. How do we reach as many as we can? Because that’s really like you know, we want to have that impact. I love the passion and – and I love the mission – that’s very, very aligned with what I’m doing so. I’M grateful so grateful to have you on the show, because I think we’re both reaching the same target audience with very similar Solutions, and I think we can do nothing but continue to add value to them to hopefully turn that into a 7030 6040 Number right to get people out of failure exactly and because I right you agree, these are like you know, people that are willing to be brave and start a company um.

You know that’s those are the best kind of people in any way that we can help right, I’m all for it. I love it, love it all right, so challenges the big problems that you know, challenges within your own company and then challenges within the companies. You work with, let’s start with your own company as you started, to build and grow this model it it. It doesn’t sound like to me a very easy Prospect of saying: okay shoot. These guys need a CMO, and these guys need a CMO, and we’ve only got three of them. How do we spread these guys out like how did you grow and build the processes to kind of adapt, your team to fit all the challenges that these new Investments are bringing to you yeah?

No, I think that, like I think, one of the biggest problems for us in the earlier stage was like. We wanted to be helpful in everything right and one that becomes like a very complicated thing to try to articulate to people right and then two. That’s a very hard thing to kind of make repeatable and scalable, and so I think we also had to be a little bit more disciplined in our offering and sort of say hey.

These are the four things that we’re going to be really good at then. We’re going to try to build a nice partner Network for when things come in, that we’re not good at and say, hey right, recommend these people to do that right and it’s like, and it’s anybody when you’re chasing.

You know, and we’ve tried to do this company very, like we’ve bootstrapped uh, which also means that, like we had to try to get everything right on the first time, which is really hard to do um, it is, it is – or at least at least partially – not Right and change it really fast right, yeah, absolutely right and that’s the thing I think like for anybody listening, that’s chasing Revenue because they need it to be sustainable.

It’s like sometimes you know, and you got to learn it from doing it, but like sometimes you bend yourself into a pretzel to get the revenue and then it would have been much more Val, faster just to get clients, yeah, just well just to get yeah. Like you know, it’s like, if you spend so much – and this is true if whether it’s a service or whether it’s a product like if you’re going to fall victim to spending so much time trying to fix a bad customer and would be much better served. Realizing that that’s not a fit being okay with it and putting that emphasis towards finding two or three new good customers love it.

I love it and so true spoken like a true bootstrapper too, you know it. It is very much no, I mean really it there’s not many of us that, like to bootstrap and I’m finding that to be more and more true. As I hear a lot of early-stage Founders thinking, okay, I’ve got a good idea. Let me go raise some money. Instead of hay I’ve, already I’ve already onboarded a handful of clients, it seems to be working. I just need some operational money right. Well, one of the things that we’re seeing a little bit more of Todd where we’ve been helpful is like taking successful services.

Companies to your point, which are, are relatively uh, investment, light to get off the ground and then having them, get some action and then, from there productizing an element of the business, either to a make their margins higher on the services side or B.

Right have a product that they can then offer at a higher margin from like more of a SAS perspective right – and I think, that’s a really compelling approach for more entrepreneurs to start doing. I love it, Adam. This has been such a fun conversation and you’re. The type of guy that I think we could probably have another hour and a half really fun conversation. You know talking back and forth about this stuff because we’re both passionate about this and for those of you listening, I highly recommend you go check out what Adams got built he’s got a really amazing platform in helping people like you bridge that gap between hey.

I just launched, and what do I do next and do I need to raise money or should I just try and keep going on this path, and I think that if you’re in those questionable moments go check out what Adam’s doing I mean really, it’s a Very, very cool site, very easy to navigate and um and Adam Before I Let You Go, I always love to get a shout out for somebody who’s. Inspired you to do what you’re doing I mean this is this is not an easy business, you’re you’re high- risk. You know business model, how are you doing it and who inspired you to get into this yeah?

I would say like if I’m goon an give a shout out I’ll, give a shout out to my dad um awesome as a father myself, that’s always good to get the shout out and I would say, like he always said, like find what you’re passionate about and The money will follow right and, like I have always been passionate about storytelling and like when I was a kid I thought I was goon can be Ernest Hemingway.

Uh turns out that I can’t drink very well um, but then I took that and so then I started telling stories as a journalist and then I realized, like I could tell corporate stories and business stories right and that has led to some Of the more financial success, but at the core, I’m still doing what I love, which means I feel like I have really worked a day in my life. I love it, love it, Adam.

Thank you. Thank you for spending time with us today and sharing these insights with our audience, and I truly hope that some people look you up and connect with you, because this really is a value, huge value, you’re adding to the world and SAS companies.

You know it’s not as easy to look sometimes in your corner, who’s advising coaching mentoring, possibly investing getting you to where you need to go without all the scrapes and scratch matches that that people like Adam, have seen so I highly advise you check them out Adam Thanks again for being here and the rest of you we’ll catch you on the next episode, thanks Adam thanks Todd, hey, I hope you enjoyed that interview with Adam. I absolutely loved it had a great post conversation with them as well. I got to record these sometime.

They we have some really good stuff.

We talked about just an amazing, founder, amazing business model and I’m telling you there are few people that I trust out there who are super aligned with wanting to just help.

He wants to help you grow, I want to help you grow and if you don’t have someone in your corner, like Adam you’ve got to have somebody or some people.

What I’m alluding to is that we have a community called the Captain’s Council captains.

Council.com is a community of CEOs and Founders who are aligned with you on their growth Journey. These are people who have successfully launched there, making money they’re generating profits, but they don’t have all the answers and where to go. Next is sometimes a really hard question to ask. So if you don’t know where to go, the best place to go is to a group of peers, other CEOs who are currently operating businesses who want to help you grow because guess what they got.

Questions too, and you might have the answers so check out Captain’s Council today, if you’re interested in collaborating with another group of CEOs who actively operating businesses are right now. This is the place to be Captain council.com. This podcast is just the first step in your growth. In trying to grow in scale, this is the first leg of the journey, and yes, it’s free. It will always be free. Our content is there to help you grow and scale. Our communities are there to help on multiple levels. No, it’s not free, but it’s so worth the money to be part of these communities and discover what it takes to grow in scale thanks.

So much for being here we’re going to catch up with you on the next one.

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Understanding Vibration and Resonance

Thanks to Curiosity Stream for sponsoring
this video. A good understanding of how structures behave
when vibrating is what allows engineers to build rotating machinery, to launch sensitive
instruments into space, and to safely design buildings in seismic areas, to name just a
few of the many applications. Systems like these can be very complex, so
to study their vibrating behaviour engineers usually start by building a simple model that
approximates the dynamics of the system, but is easier to assess. The two most important parameters in any vibrating
system are its mass and its stiffness. A common modelling approach is to lump all
of the different contributions to mass and stiffness together, and represent them using
a point mass with a mass m and a spring with a stiffness k. This is called the lumped parameter modelling
approach. This kind of simplified model might seem quite
abstract, but can actually represent the dynamic behaviour of a lot of real systems quite accurately. The beauty of this simplicity is that we now
have something that we can analyse mathematically.

But first we have to make a few assumptions. We'll assume that the mass can only move up
and down. Since the system behaviour is defined by a
single output, the x coordinate of the mass, this is what's called a single degree-of-freedom
model. We'll also neglect the effects of gravity,
and for now we'll assume that there's no damping, meaning that no energy is lost from the system
as it vibrates, by friction or other means.

No external loads are acting on the system
– the purpose of the model is to understand how the system behaves in free vibration,
or in other words how it will oscillate when it's displaced, and then released. Since we've assumed there's no damping, the
mass will continue to oscillate like this indefinitely. The way the system vibrates is defined by
its equation of motion, which can be determined by applying Newton's second law. The second law states that the sum of the
forces acting on the point mass is equal to the product of its mass and its acceleration,
F=ma. We can figure out the sum of the forces acting
on the mass by drawing a free body diagram.

There is only one force, the force exerted
by the spring, which is equal to the displacement x multiplied by the spring stiffness k. And
so we obtain the equation of motion for the system. This is an ordinary differential equation,
and the solution is a sinusoidal function. t is time, Phi is the phase angle and A is
the amplitude of vibration. We can determine A and Phi by considering
the initial position and velocity of the mass. Let's look at an example where the system
has a mass of 5 kilograms and a spring stiffness of 20 Newtons-per-metre, and vibration is
triggered by applying an upwards velocity of 2 centimetres per second to the mass. Since the displacement x is initially zero,
the phase angle Phi must also be equal to zero. And then we can differentiate the equation
for x to calculate the amplitude of vibration A. An important property that can be calculated
from a mass-spring model is the system's natural frequency, the frequency at which it will
oscillate naturally when in free vibration. It's given by this term in the solution to the equation of
motion, and is denoted using the Greek letter Omega.

It depends only on the mass and the spring
stiffness, so no matter what the initial conditions are a system will always oscillate at the
same frequency. It has units of radians per second, so is
called the angular natural frequency. But it's sometimes more practical to think
of the natural frequency as a number of cycles per second, in which case it's denoted using
the letter f and has units of Hertz. The inverse of the natural frequency is the
period T, which is the duration of each cycle in seconds. Let's compare how two different systems oscillate. Both of these models have the same spring
stiffness, but different masses, and so different natural frequencies. The heavier mass oscillates at a much lower
frequency. A neat demonstration of the natural frequency
is the tuning fork. When the fork is struck it vibrates at its
natural frequency, which is much faster than shown here.

This causes the air molecules to vibrate at
that same frequency, which produces a corresponding tone. By assuming that the prongs behave like cantilever
beams in bending, beam theory can be used to derive a formula for the natural frequency
of the fork. The density, length and cross-section of the
prongs can be calibrated to obtain the desired tone. Of course when a mass oscillates freely it
doesn't do so indefinitely. Energy within the system is dissipated as
heat over time, so the oscillations progressively decrease in magnitude and eventually stop
altogether. This loss of energy is called damping, and
it occurs in all real mechanical systems. There are several different mechanisms that
can contribute to the overall damping of a system.

With structural damping, energy in a vibrating
structure is dissipated due to the relative motion of components at structural joints. And material damping is damping provided by
the material itself, where energy dissipates in a vibrating material due to interactions
occurring at the molecular level. To improve our spring-mass model, we can lump
the damping from all of the different sources together, and represent them by a single dampening
device called a dashpot, which is essentially a plunger that moves through a liquid-filled
cylinder. Whenever the plunger moves a force will act
to oppose its displacement, and the magnitude of this damping force is proportional to the
velocity of the displacement – the faster the plunger moves, the larger the damping
force. C is the viscous damping coefficient – it
defines the total amount of damping in the system. This model of damping is called viscous damping,
because it behaves in a similar way to viscous forces in a fluid, which are proportional
to the fluid velocity. There are other damping models, but viscous
damping is commonly used because of its simplicity.

If we include the dashpot in our spring-mass
model, the equation of motion is the same as for the undamped system, but also includes
the damping force. It's a little more difficult to solve this
equation, and the solution will depend on the amount of damping. If a system is underdamped, it will oscillate,
and the magnitude of each successive oscillation will decrease until it stops. If the damping of the system is increased
significantly, which you can think of as the dashpot being filled with a far more viscous
fluid, any oscillation will be completely suppressed by the damping. This is called an overdamped system. And a critically damped system occurs right
at the limit between these two cases – it has just enough damping to suppress vibration. Each of these cases has a different function
that defines the displacement of the system, obtained by solving the equation of motion. The ratio of the actual damping coefficient
of the system to the damping coefficient that would result in a critically damped response
is the damping ratio. Most engineering systems and structures have
a damping ratio of less than 1, so they’re underdamped.

Of course if we're modelling a real system
we need a way of figuring out which value to use for the damping coefficient. It usually has to be determined experimentally,
and one way of doing this is by measuring the displacement of the system as it oscillates. A parameter called the logarithmic decrement
can be calculated based on this test data, as the natural logarithm of the ratio of any
two successive amplitudes. The damping ratio can be calculated from the
logarithmic decrement, providing an estimate of the overall damping in the system. So far we've looked at free vibration, where
oscillation is only caused by the initial conditions – there are no externally applied
loads. But another scenario is forced vibration,
where oscillation is driven by an external force. This type of loading often occurs in rotating
machinery. A common problem with turbines and motors
occurs when a rotating component is unbalanced, meaning that its mass is unevenly distributed. This introduces a load that has a sinusoidal
component in the vertical direction, and can cause vibration.

Unbalance can occur because components were
poorly fabricated or have been distorted. But eccentric masses are sometimes added to
motors on purpose – intentionally unbalanced motors are how phones and video game controllers
are able to vibrate. We can analyse this type of forced vibration
using the spring and dashpot model, by adding a sinusoidal external load. The resulting equation of motion is similar
to the free vibration case, but is a non-homogeneous differential equation. Its solution is the sum of two functions – a
complementary solution and a particular solution. The complementary solution is the solution
to the homogeneous form of the equation, where the right hand side is equal to zero. This is just the solution to the equation
of motion for an underdamped system in free vibration that we saw earlier.

And the particular solution captures the effect
of the external loads and is given by this expression. R is the ratio of the frequency of the external
force to the natural frequency of the model. Since there's damping in the system, the complementary
solution that represents free vibration will eventually reduce to zero. At this point the motion of the system is
defined by the particular solution only. For this reason the particular solution describes
what's called the steady-state response. It has the same frequency as the forcing function,
but is offset by a certain phase angle, meaning that the response of the system lags the external
force. Something interesting happens to the steady-state
response when the frequency of the forcing load is very close to the natural frequency
of the system. R approaches 1, and so the first term in the
square root is close to zero. And if the system has very little damping
the second term will also be close to zero, which means that the displacement will become
very large.

Let's plot the normalised maximum displacement
against the frequency ratio. For an undamped system the damping ratio is
equal to zero, so when the forcing and natural frequencies match, the displacement becomes
infinite. All systems have some level of damping, so
this is just a theoretical case – here's what the response looks like for different damping
ratios. We can see this effect if we adjust the speed
of the unbalanced motor. As the frequency of the force caused by the
eccentric mass approaches the natural frequency of the system, the displacements become very
large. This happens because when the natural frequency
and forcing frequency are the same, the energy added to the system by the external force
is timed just right so that it increases the amplitude of the displacement with each cycle.

This is called resonance. Resonance can be very dangerous and needs
to be assessed carefully. It's one of the reasons it's so important
to be able to calculate the natural frequency of a system. If the natural frequency of a bridge matches
the frequency of wind loading acting on it, or of pedestrians crossing it, the results
can be catastrophic, particularly if the structure has little damping. Devices called tuned mass dampers are sometimes
installed in buildings and bridges to control the dynamic response at resonant frequencies. With a rotating eccentric mass the external
force acting on the system is a simple sine wave function.

This makes it easy to solve the equation of
motion, since we can obtain a neat closed-form solution. But if the loading is defined by a complicated
function, or is completely arbitrary, which might be the case if it's based on test data,
it might not be possible to solve the equation of motion directly, and numerical integration
methods will have to be used instead. Designing a structure to withstand seismic
events is difficult because the loading caused by an earthquake is random and can't be predicted
ahead of time. And so engineers have to use special probabilistic
techniques like the response spectrum method to design structures to withstand seismic
loads. Single degree of freedom models are really
useful, but sometimes the dynamics of a system are better modelled using multiple degrees
of freedom. Say we want to model the dynamic response
of a three storey building. If we assume that the columns between the
floors are axially rigid but can bend laterally, we can model it as a system with three degrees
of freedom, the x coordinate of each floor. Each of the masses in the model has its own
equation of motion, and if we rewrite this system of equations in matrix form we can
see it has the same familiar form as the equation of motion for an undamped single degree-of-freedom
system.

A single degree-of-freedom system has one
natural frequency and can only vibrate in one way. But since our model has three degrees of freedom
it will also have three natural frequencies, and at each natural frequency the system will
vibrate in a specific way, which is called a mode shape. Exactly how the system vibrates in practice
will depend on the initial conditions that are applied. For the three storey building the three modes
of vibration will look like this. As the number of degrees of freedom increases
it becomes necessary to use numerical techniques like the finite element method to determine
the natural frequencies and associated mode shapes. We've only covered mass-spring models in this
video, which oscillate by translating. But there are other types of vibration too,
like pendulums, which oscillate by rotating. This video is long enough already, but I've
published a short companion video that covers the motion of pendulums over on Nebula, where
we take a look at how the motion of a pendulum differs from a mass-spring system and how
to derive the equation of motion. Nebula is a streaming service built by a group
of educational creators, which means it's completely free of ads, and revenue generated
by the project is distributed directly to the creators.

It's full of curated independent content,
including Nebula originals and bonus content you won't find anywhere else. And if you're in the mood for expertly made,
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Patterns in raising 1 and -1 to different powers | Pre-Algebra | Khan Academy

Let’s think about exponents with ones and zeroes. So let’s take the number 1 and let’s raise it to the eighth power.

So we’ve already seen that there’s two ways of thinking about this.

You could literally view this as taking eight 1’s and then multiplying them together.

So let’s do that.

So you have one two, three, four five, six, seven, eight 1’s and then you’re going to multiply them together And if you were to do that, you would get well 1 times.

1 is 1 times 1.

It doesn’t matter how many times, you multiply 1 by 1.

You are going to just get 1, You are just going to get 1 And you could imagine I did it eight times.

I multiplied eight 1’s, But even if this was 80 or if this was 800 or if this was 8 million.

If I just multiplied 1, if I had 8 million 1’s and I multiplied them all together, it would still be equal to 1. So 1 to any power is just going to be equal to 1 And you might say, hey what about 1 to the 0 power.

Well, we’ve already said anything to 0 power, except for 0 that’s, where we’re going to it.’s actually up for debate, But anything to the 0 power is going to be equal to 1 And just as a little bit of intuition.

Here you could literally view this as our other definition of exponentiation, which is you start with a 1, and this number says how many times you’re going to multiply that 1 times.

This number So 1 times 1 zero times is just going to be 1, And that was a little bit clearer when we did it like this, where we said 2 to the let’s say, fourth, power is equal to this was the other definition of exponentiation.

We had, which is you start with a 1, and then you multiply it by 2, four times so times, 2 times 2 times 2 times 2, which is equal to let’s see.

This is equal to 16.

So here, if you start with a 1 and then you multiply it by 1 zero times, you’re still going to have that 1 right over there And that’s.

Why anything that’s not 0 to the 1 power is going to be equal to 1? Now let’s try some other interesting scenarios.

Let’s start try some negative numbers.

So let’s take negative 1 And let’s first raise it to the 0 power. So once again, this is just going based on this definition.

This is starting with a 1 and then multiplying it by this number 0 times.

Well, that means we’re just not going to multiply it by this number.

So you’re just going to get a 1.

Let’s try negative 1.

Let’s try negative 1 to the first power.

Well, anything to the first power.

You could view this, and I like going with this definition as opposed to this one right over here.

If we were to make them consistent, if you were to make this definition consistent with this, you would say: hey let’s start with a 1 and then multiply it by 1 eight times, And you’re still going to get a 1 right over here.

But let’s do this with negative 1, So we’re going to start with a 1 and then we’re going to multiply it by negative 1 one time times negative 1, And this is of course going to be equal to negative 1. Now let’s take negative 1 and let’s take it to the second power.

We often say that we are squaring it when we take something to the second power, So negative, 1 to the second power.

Well, we could start with a 1.

We could start with a 1 and then multiply it by negative 1.

Two times multiply it by negative 1 twice And what’s this going to be equal to And once again by our old definition.

You could also just say: hey ignoring this one, because that’s not going to change the value.

We took two negative 1’s and we’re multiplying them Well negative 1 times negative 1 is 1 And I think you see a pattern forming.

Let’s take negative 1 to the third power.

What’s this going to be equal to? Well, by this definition, you start with a 1 and then you multiply it by negative 1, three times so negative 1 times negative 1 times negative 1 Or you could just think of it.

As you’re taking three negative 1’s and you’re multiplying it because this 1 doesn’t change the value, And this is going to be equal to negative 1 times. Negative 1 is positive 1 times negative 1 is negative.

1.

So you see the pattern Negative 1 to the 0 power is 1 Negative.

1 to the first power is negative 1.

Then you multiply it by negative 1.

You’re going to get positive 1.

Then you multiply it by negative 1 again to get negative 1 And the pattern you might be seeing is, if you take negative 1 to an odd power, you’re going to get negative 1 And if you take it to an even power, you’re Going to get 1 because a negative times a negative is going to be the positive And you’re going to have an even number of negatives so that you’re always going to have negative times negatives.

So this right over here.

This is even Even is going to be positive, 1, And then you could see that if you went to negative 1 to the fourth power Negative 1, the fourth power.

Well, you could start with a 1 and then multiply it by negative 1 four times. So a negative 1 times negative 1 times negative 1 times negative 1, which is just going to be equal to positive 1.

So if someone were to ask you, we already established that if someone were to take 1 to the I don’t know 1 millionth power.

This is just going to be equal to 1.

If someone told you let’s take negative 1 and raise it to the 1 millionth power.

Well, 1 million is an even number, so this is still going to be equal to positive 1.

But if you took negative 1 to the 999 999th power, this is an odd number.

So this is going to be equal to negative 1 .

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Understanding the Finite Element Method

Thanks to CuriosityStream for sponsoring this
video. There are a lot of different analytical methods
that engineers can use to solve structural mechanics problems, whether it's to calculate
the deflection of a beam or the stresses in a flat plate. But we often encounter problems that can't
be solved in this way, typically because the geometry, loads or materials are too complex. The finite element method is a powerful
numerical technique that uses computational power to calculate approximate solutions to
these types of problems. It's widely used in all major engineering
industries. It could be used to check that satellite components
will survive the launch conditions, for example. Or to optimise the design of automotive components,
like the lower control arm of this car's suspension system. Finite element analysis software can be used
to analyse a wide range of solid mechanics problems, including static, dynamic, buckling,
and modal analyses.

But it can also be used for fluid flow, heat
transfer, and electromagnetic problems. For this introduction to the finite element
method, we'll focus on how it applies to static linear-elastic stress analysis. Imagine we want to analyse the brackets supporting
this air conditioning unit. The goal of a static stress analysis would
typically be to calculate the stresses, strains and displacements within the bracket. These unknowns are called "field variables". Internal stresses develop within a body in
such a way as to maintain equilibrium over any volume of the body, so we can apply the
concept of equilibrium to calculate the field variables. This is easy to do for a simple beam – we
can use equilibrium to calculate the bending moment and shear force along it, and from
there we can calculate the normal and shear stresses in the beam.

But enforcing equilibrium over a two dimensional
shape like this bracket is difficult, and it becomes even more complicated for a three
dimensional body. The finite element method approaches this
problem by splitting the body into a number of small elements, that are connected together
at nodes. This process is called discretisation, and
the collection of nodes and elements is called the mesh. Discretisation is useful because the equilibrium
requirement now only needs to be satisfied over a finite number of discrete elements,
instead of continuously over the entire body. Several different element shapes can be used. We've used triangular surface elements to
model this bracket. Surface elements are two dimensional elements
that are typically used to model thin surfaces. They can be triangular or quadrilateral. Triangular elements are good for modelling
awkward shapes, although quadrilateral elements tend to perform better. Solid elements are used for three-dimensional
bodies.

And then we have line elements. Choosing the right element for your model
will depend on the specific scenario being analysed, and requires some expertise. In the case of our bracket we could have used
solid elements, or even line elements, depending on how much we wanted to simplify the problem. Even for elements of the same shape, there
are hundreds of different types to choose from that each have different formulations,
and introduce different levels of approximation. A line element can be a bar, for example,
that only carries axial loads, or a beam, that can carry axial, bending, shear and torsional
loads. We can model the bracket using plane stress
surface elements, because the bracket is thin and the loading is all in the same plane.

But that's only one of many surface element
types. These are all first order elements, but we
can also use second order elements, which have additional mid-side nodes and are more
accurate. For stress analysis problems the fundamental
variable we want to calculate is the displacement at each node. If we know how a body displaces when loads
are applied, we'll easily be able to calculate secondary outputs like stress and strain. For each element we can define a vector {u}
that contains all of the possible displacements for the nodes of the element, including rotations.

If we're analysing a two-dimensional case
with beam elements, each node can translate along the X and Y axes and it can rotate about
the Z axis, so the vector {u} will look like this. Each of these displacements is called a degree
of freedom. For the beam element we have 3 degrees of
freedom per node, or 6 in total. For a 3D case that increases to 6 degrees
of freedom per node. A shell element node also has 3 degrees of
freedom in two dimensions, but since the element has 4 nodes, it has 12 degrees of freedom
in total. The nodes of a solid element only have the
3 translational degrees of freedom.

The nodes aren't allowed to rotate and instead
rotation of the element is captured by translation of the nodes. So how can we calculate all of the displacements
at every node in our mesh? For a spring, the relationship between force
and displacement is defined by Hooke's law. The spring stiffness k determines how far
the spring will displace for a given force. In the same way, we can think of the elements
of our mesh as having a certain amount of stiffness, that resists deformation. In this equation {f} is a vector of the nodal
forces and moments, {u} is the vector of the nodal displacements, and [k] is the stiffness
matrix of the element. A 2D beam element has 6 degrees of freedom,
so the displacement vector looks like this.

And the force vector and the stiffness matrix
will look like this. The element stiffness matrix defines how much
each node in the element will displace for a set of forces and moments applied to the
nodes, and so is the key to solving the displacements at every node of our mesh. It's a square matrix – the number of rows
and the number of columns are equal to the number of degrees of freedom of the element. We can figure out what the terms of the stiffness
matrix are by enforcing equilibrium. We'll come back to this later on in the video,
but for a 2D beam the matrix looks like this. We can think of this equation as a system
of linear equations that we can solve to obtain the displacements at the nodes of our mesh. If we apply a lateral displacement to node
2, for example, and all of the other degrees of freedom are fixed, and so are equal to
zero, we can use the stiffness matrix to calculate the forces and moments at both of the nodes. To make the next steps easier to visualise,
let's represent the stiffness matrix in a more abstract form.

This is just one element, but our overall
mesh will be made up of many more elements. Let's look at a simple example where we have
a mesh made up of three 2D beam elements, that we're using to model a cantilever beam. We can assemble the individual stiffness matrices
for all of the elements in our mesh into a huge global stiffness matrix that defines
how the entire structure will displace when loads are applied to it. Like the element stiffness matrix, the global
stiffness matrix is a square matrix and the number of rows and columns is equal to the
total number of degrees of freedom in the model. The element stiffness matrices are assembled
together to form the global stiffness matrix based on how the elements are connected together. Elements 1 and 2 are connected at node 2 for
example. Continuity tells us that since these two elements
are connected at the same node, the displacements for both elements must be the same at the
common node. So when we assemble the global stiffness matrix,
the terms in the element stiffness matrices corresponding to node 2 should be summed for
each degree of freedom.

Element 3 is not connected to node 2, so this
element's stiffness matrix should have no effect on the displacements at node 2. This is what the actual global stiffness matrix
looks like for this model. It has some interesting characteristics. It is said to be sparse, because it contains
a lot of zeros, and banded, because the non-zero terms are grouped around the diagonal. For linear-elastic problems the matrix will
also be symmetric. If we modify the mesh so that the three elements
are connected differently, the global stiffness matrix will change. In this case we have three nodes instead of
four, so the matrix will be smaller, and the fact that elements 1 and 3 are connected is
reflected in the matrix. An important thing to note here is that the
elements are no longer aligned to the same coordinate system, so we have to transform
the stiffness matrix for each element so that it aligns with a global coordinate system.

We can do this by multiplying each element
stiffness matrix by a rotation matrix. Now that we've assembled the global stiffness
matrix, we need to solve this equation to obtain the displacements at each of the nodes. To do this we need to define the external
loads, and the boundary conditions. The boundary conditions are known displacements
at specific nodes, typically because specific degrees of freedom are fixed. In this model, vertical and horizontal translations
are fixed at node 1, and vertical translations are fixed at node 2, so the displacement vector
looks like this. And the force vector will look like this. It includes the applied force and the reaction
forces at the supports. Now we can solve the equation. We could do this by inverting the global stiffness
matrix and solving the displacements from there.

But in practice inverting the matrix isn't
very efficient, particularly because it's a sparse matrix. Commercial solvers mostly use methods that
involve iteratively approximating the displacement vector, like the conjugate gradient method. Once we've solved for the nodal displacements,
we can calculate the strains and then stresses throughout the mesh. A typical finite element mesh could easily
have a hundred thousand degrees of freedom, which would be impossible to solve by hand,
and so applying the finite element method to anything more complicated than a very basic
model requires the use of appropriate software. Now that we have an overall understanding
of the finite element method, let's return to the element stiffness matrix to see how
it's derived.

The matrix shown here is for a 2D beam element,
but it will look very different for different element types. Several different methods can be used to derive
these stiffness matrices, and they are all fundamentally based on the concept of equilibrium. The direct method derives the stiffness matrix
directly from the equilibrium equations that govern the behaviour of the element. The lateral deflection of a beam is governed
by this equation, for example, so we can solve the equation to obtain the stiffness matrix
for a beam element. These governing equations are usually differential
equations. The differential equations and associated
boundary conditions are what we call the "strong" form of the equilibrium problem. But it's only really possible to solve the
strong form for simple elements. For more general cases we can use "weak" forms
that describe the differential equations in integral form, instead of solving the differential
equations directly. These give approximate solutions to the equilibrium
equations, but are easier to solve.

The first of the weak form methods is based
on variational principles. One such principle commonly used for structural
mechanics problems is the Principle of Minimum Potential Energy. It states that the displacement configuration
that satisfies equilibrium conditions is the one that minimises the total potential energy,
where the potential energy is the sum of the strain energy and the potential energy of
the external loads. By applying a mathematical technique called
the calculus of variations to minimise the total potential energy, we can obtain an approximate
solution to the equilibrium equations.

The other weak form method is the Galerkin
method of weighted residuals. In this method the function that satisfies
the differential equation is approximated as the sum of a number of assumed trial functions
that each have unknown coefficients. This approximate solution is substituted into
the differential equation, and an equation for the error, called the residual, is obtained. If we multiply each trial function by the
residual and set the integral of this product to zero, we can calculate the unknown coefficients
that minimise the residual. This gives us an approximate solution to the
differential equation.

This is a more widely applicable approach
than the principle of minimum potential energy, but for stress analysis problems both methods
give the same result. Regardless of which method we use, we end
up with the stiffness matrix for our element. But to apply these methods we need to be able
to describe how displacements and other field variables vary inside the element, instead
of just at the nodes of the element. To overcome this issue, an element needs to
have a defined function that calculates values inside the element by interpolating the values
at the nodes.

The shape function is just an assumption. It's usually chosen to be a polynomial, since
they're relatively simple and sufficiently accurate. And with that we've covered all of the key
aspects of the finite element method. In summary, the first step in the finite element
method is defining the problem, including the relevant material properties, loads and
boundary conditions. Next the body being analysed is split into
a number of small elements connected at nodes, and the element types are chosen. Then a stiffness matrix is defined for each
element, using one of the three methods we covered earlier. The element stiffness matrices are then assembled
into a global stiffness matrix based on element connectivity. This global stiffness matrix defines how the
structure will respond to applied loads, and we can use it along with boundary conditions
to solve for the displacement at each node in the structure.

Once we have displacements we can calculate
stresses, strains and other field variables of interest. Then all that's left to do is post-processing
to obtain the desired results, and validation of the model. A lot of the hard work like calculating the
element stiffness matrices, assembling the global stiffness matrix and solving the model
is done by the software being used. But the engineer is responsible for making
sure that the problem has been properly defined, that the mesh is suitable, and for interpreting
and validating the results. I hope this video has helped you develop a
better understanding of the fundamentals of the finite element method. If you're interested in learning more, you
can check out the extended version of this video, that's available now over on Nebula,
where I spend a few more minutes covering the problem definition, discretisation, post-processing,
and validation steps. Nebula is a streaming service built by independent
educational creators.

It's a place where you can find extended versions
of my videos, alongside amazing original content from other creators, like Mustard and Wendover,
without any ads or sponsor messages. You can get access to Nebula for free when
you sign up for CuriosityStream. CuriosityStream is the perfect streaming service
for curious minds. It has thousands of high quality documentaries
to keep you entertained and learning, like Particle Fever, an incredible film that follows
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And that's it for this introduction to the
finite element method. Thanks for watching!.

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Different types of shares | Video 1. DSCG1 UE6. Finance. Stocks and Shares.

one ordinary shares the most common type of shares are known as ordinary shares purchasing ordinary shares gives the owner of stake in the company and an entitlement to dividends dividends are the part of the company's profits that are paid out to the shareholders every six months when the company is making a profit most ordinary shares also give the shareholder a right to attend the company's Annual General Meeting and vote on issues relevant to the company's future to preference shares preference shares return a fixed dividend to the investor that is not linked to the company's annual profit result although preference shareholders receive dividends before ordinary shareholders they do not receive the same voting rights as ordinary shareholders three contributing shares contributing shares of those that have not been fully paid for and require further payment in the future dividends are generally paid according to the proportion of the paid up amount for bonus issues a bonus issue is a free issue of new shares to existing shareholders every now and then when a company makes an extraordinary profit or if it is amassed accumulated profits over a period of time it gives its shareholders a present of a bonus issue of shares at no cost receiving a bonus issue does not increase the proportion of a company owned by the shareholder as all shareholders receive the same present in proportion to their ownership of the company it is in effect a cashless dividend five rights issues a rights issue is also an issue of new shares to existing shareholders however these are not free a rights issue occurs when a company needs to raise extra capital and it gives its shareholders our right but not an obligation to purchase extra shares there are two types of rights issues renowned scible and non renowned civil rights pronounceable rights can be traded on the share market if an existing shareholder does not wish to purchase the new shares being offered to them they are therefore of some value to the shareholder a little bonus non renowned scible rights cannot be traded or sold to others so if the shareholder does not take up their right to buy the new shares by a particular date the writer of no value to them so those are the five main types of shares in general when we refer to shares in this and other training modules we are talking about ordinary shares you

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