# Homework Help: Springs and potential/kinetic energy

1. Dec 8, 2015

### Carrie

1. The problem statement, all variables and given/known data
A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position.

(a) What is the amplitude of vibration?
I already solved for the amplitude and got 0.24 meters.

(b) At what location are the kinetic energy and the potential energy the same?
???

2. Relevant equations
E = 1/2mv^2 + 1/2kx^2

3. The attempt at a solution
E = 1/2mv^2 + 1/2kx^2

I thought I would set the kinetic energy and potential energy equal to each other, so I got:

1/2(.5)(1.5)^2 = 1/2(20)x^2
From that, I got x = .24 meters.

But that's wrong and the answer is 0.17 meters. I'm confused as to where I went wrong. :(

Thank you!!

2. Dec 8, 2015

### TSny

Why did you use 1.5 m/s for the speed here?

3. Dec 8, 2015

### Carrie

Oh, the 1.5 m/s is for the equilibrium position, which I guess isn't necessarily the same position?

4. Dec 8, 2015

### TSny

Right. The location where the KE equals the PE is not the equilibrium position.

5. Dec 8, 2015

### Carrie

I'm sorry, but now I'm really lost. How do I find v then, or am I using the wrong the wrong equation or something?

6. Dec 8, 2015

### TSny

What can you say about the total energy E at different points of the motion?

7. Dec 8, 2015

### Carrie

The total energy stays the same.

8. Dec 8, 2015

### TSny

Yes. If you pick any two points of the motion, then E is the same for those two points. You probably used that idea when answering part (a).

See if you can use the same idea to help solve (b).

9. Dec 8, 2015

### Carrie

Ohhh okay, so if at equilibrium, the total energy (when PE is 0) is 1/2 mv^2, which is 0.56 J, then when they're the same:

0.56 (total energy in the system) = 2* 1/2kx^2 - I'm not sure if the theory is right, but since KE = PE, then KE+PE becomes PE + PE and so you can multiply by two. Maybe. Because I did get the answer this way, but I also want to make sure I didn't just get lucky.
x = 0.17 m.

10. Dec 8, 2015

### TSny

You are thinking correctly. Good work.

11. Dec 9, 2015

### Carrie

Awesome!! Thank you so much for your help!