Hey, guys. Let's take a look at this example. So we're told that the velocity of a particle is given by this equation, and that's the only thing that we're given, and we're supposed to find out what the frequency of motion is. So what they're asking us is to figure out what f is. Let's take a look at my equation list. The only equation that involves frequency is the big omega equation right here. The problem is I don't have any of those other variables. I don't have k over m, I don't have the period, and I don't know what the omega is either. The only thing I am given is just the velocity equation. Let's take a look at the actual velocity equation with all the variables involved. So I've got the velocity is equal to negative 6 times the sine of 3 pi times t. But the form of the equation is I have negative a omega, and I've got sine of omega times t. So if you just look at this, what is this telling us? Well, we've got this negative 6 out here, and I've got a negative a omega. So that means that these things are equal to each other. So that means I have that a omega is equal to 6. And if you look inside the parentheses, I've got this omega over here that's equal to this 3 pi. So those two things are the same. So that means that omega, what they're telling me, is equal to 3 pi. Now let's take a look at my frequency equation. I don't have the period and I don't have the square root of k over m, but now I do have the omega. So let's relate that equation. So I've got omega is equal to 2 pi times the frequency, but omega, I just figured out was 3 pi. So I'm gonna set these 2 things equal to each other. So 2 pi times the frequency equals 3 pi, and now the frequency is just 3 pi over 2 pi, and what'll happen is the pi's will cancel, and so I get frequency like, the actual form of the equation to figure out what those things are. Let's look at part b. Part b is now asking us for the amplitude. So great. How do we find out the amplitude? We've got a bunch bunch of equations that involve the amplitude. So let's take a look. I'm not told the x max, v max, or a max. I'm never told any of those things, and I don't know what the a max or the restoring force is, so I can't use that. So I'm gonna have to again look at this equation right here. And from this equation, I figured out that A omega was equal to 6. So let's write that out. If A omega is equal to 6, then a is just going to be 6 divided by omega. But I figured out what omega was as well. Remember that omega was just equal to 3 times pi right over here. So that means that the amplitude is just 2 over pi once you go ahead and solve that. So I've got that's the amplitude, 2 over pi. Now for this last one, I'm supposed to find out what the velocity is at a specific time. So this is a question where they're giving me t and I've asked for v, so I'm just going to basically plug them into my formula. So the velocity when t is equal to 0.5 seconds is gonna be negative 6 times the sine of 3 pi times 0.5. Make sure that you're in radians mode, and you should get a velocity that's equal to 6 meters per second. And that's it. Let me know if you guys have any questions, and if not, let's keep going.
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17. Periodic Motion
Intro to Simple Harmonic Motion (Horizontal Springs)
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Intro to Simple Harmonic Motion (Horizontal Springs) practice set
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