# Homework Help: Total energy of a spring-mass system (harmonic motion)

1. Jan 30, 2008

### Terp

Hi all. I've this problem and I'm stuck on the part where I have to find the total energy.

1. The problem statement, all variables and given/known data
A 507 g mass oscillates with an amplitude of 10 cm on a spring whose spring constant is 20 N/m. At t =0s the mass is 5.0 cm to the right of the equilibrium position and moving to the right.

2. Relevant equations

E = K + U = (1/2)mvx^2 + (1/2)kx^2

I've already figured out the period to be 1.00s, the angular frequency is 6.28 rad/s, phase constant is -1.05 rad, initial velocity is .544 m/s, and final is .628 m/s. I know all of these to be correct.

3. The attempt at a solution

Using the equation above and plugging numbers in I get:

(1/2)(.507kg)(.544^2) + (1/2)(20Nm)(5.0cm^2) = 250.075J but this online homework thing says it's wrong. Should I use E = (1/2)m*vmax^2? That only gives .09J.

Anybody have any clue? Thanks a lot!

Last edited: Jan 30, 2008
2. Jan 30, 2008

### Noein

3. Jan 30, 2008

### Terp

Thanks for the reply. I noticed that the 5.0cm isn't in meters, I changed it to .05m, which changed the resulting energy to 0.100J, but that seems low.

4. Jan 30, 2008

### Staff: Mentor

Why not choose another point to compare? Hint: Find the energy when it's at max amplitude.

5. Jan 30, 2008

### Terp

That would mean E = 1/2kA^2 = (1/2)*20*.10^2 = .1J. Does that sound correct? It seems too small to be correct.

EDIT: Now that I think about it, .5kg isn't very heave and .544 m/s is pretty darn slow.

Last edited: Jan 30, 2008
6. Jan 30, 2008

### Staff: Mentor

Sounds good to me!

7. Jan 30, 2008

### Terp

That was right, thanks a lot! I feel like a tard now! :)