Relate simple harmonic motion to circular motion

[peanut15]

1. Prove that the maximum speed of a mass on a spring is given by Vmax = 2pifA
f = frequency A= amplitude

We have just learned how to relate simple harmonic motion to circular motion. So I am dealing with some of those equations.

3. While writing this out I kind of had a thought and think I got it, but am still not sure.

T=2pir/V is one of the equations that we are shown.
we are also shown that A=r because of the radius being a circles maximum amplitude. so
T=2piA/V
V=2piA/T and T=1/f right?
so
V=2pifA ?

Is this correct?

 

[berkeman]

1. Prove that the maximum speed of a mass on a spring is given by Vmax = 2pifA
f = frequency A= amplitude

We have just learned how to relate simple harmonic motion to circular motion. So I am dealing with some of those equations.

3. While writing this out I kind of had a thought and think I got it, but am still not sure.

T=2pir/V is one of the equations that we are shown.
we are also shown that A=r because of the radius being a circles maximum amplitude. so
T=2piA/V
V=2piA/T and T=1/f right?
so
V=2pifA ?

Is this correct?

Welcome to the PF. I didn't follow what you wrote... Have you had beginning calculus yet? If so, write an equation for the displacement of the mass as a funtion of tiime. It will have an oscillatory term with a sin() or cos() in it (your choice). If that is the equation for the displacement, how can you use calculus to find the equation for the velocity as a function of time? That will show you how to get the answer they are asking about.

 

[peanut15]

Welcome to the PF. I didn't follow what you wrote... Have you had beginning calculus yet? If so, write an equation for the displacement of the mass as a funtion of tiime. It will have an oscillatory term with a sin() or cos() in it (your choice). If that is the equation for the displacement, how can you use calculus to find the equation for the velocity as a function of time? That will show you how to get the answer they are asking about.

They would have talked about calculus if I had to use it to do a proof of this. I don't think it is required and there are no trig functions at all. I have taken calculus and would be looking for a solution that way, but they would usually demonstrate something mathmatical like that before asking us to use it in a solution.

I could list out all the equations they give on the page before that should be used to solve this question. They were all about relation simple harmonic motion to circular motion. Which would be where the 2pi comes from into the simple harmonic motion of the spring.

 

[berkeman]

They would have talked about calculus if I had to use it to do a proof of this. I don't think it is required and there are no trig functions at all. I have taken calculus and would be looking for a solution that way, but they would usually demonstrate something mathmatical like that before asking us to use it in a solution.

I could list out all the equations they give on the page before that should be used to solve this question. They were all about relation simple harmonic motion to circular motion. Which would be where the 2pi comes from into the simple harmonic motion of the spring.

I was trying to get you to think about what is really going on physically, not about what canned equations they may have listed for you.

Can you write the equation for the x displacement of the mass? You are correct that the mass moves in simple harmonic motion. That is where the sin() or cos() funtion comes in. You don't need the circle analogy at all, just write the equation for x(t), and use simple differential calculus to find v(t). Very simple and physical way to show what they are asking for.