# Homework Help: Mechanical energy of a mass-spring system

1. Apr 4, 2005

### Hit an Apex

Hey,
Stuck on finding the mechanical energy of a mass-spring system, my question is as follows > A mass-spring system oscillates with an amplitude of .026 m. The spring constant is 290 N/m and the mass is 0.50 kg, it asks for the mechanical energy in (J). and the maximum acceleration of the mass-spring system which is 15.08 m/s (verified, webassign rules).

Mechanical energy is confusing to me, I am pretty determined it might be potential(PE)enery + kinetic energy(KE), but ofcourse the formula for KE involves velocity. I only have the acceleration so I feel I have gone astray along the way.

Basically I am having trouble finding where to start and then I'm wondering how to get the answer in Joules.

Thanks.

2. Apr 4, 2005

### Skomatth

The mechanical energy of a mass-spring system with speed v at position x is $$E = .5mv^2 + .5kx^2$$ .

Pick a point in the oscillation and apply this equation. (Hint: there's a special point in its motion which simplifies this problem greatly).

3. Apr 4, 2005

### Hit an Apex

Thanks for the reply. I assume when you say pick a point you mean pick a point to plug in for the variable V. The amplitude is .026m

So far I have this

E=.25v^2 + 0.09802

Would V be 1/2 of the maximum acceleration?

4. Apr 4, 2005

### Skomatth

When the mass it as its maximum displacement what is its velocity? You should know this without having to use a formula. If you don't, review the chapter.

Last edited: Apr 4, 2005
5. Apr 4, 2005

### Hit an Apex

The chapter has been read very carefully by me twice. We haven't really covered mass at its maximum displacement, or maybe we have and called it something else.

I think by maximum displacement you mean the amplitude which is ofcourse .026m. Maximum accel. is 15.08 m/s . I realize the answer is probably smack in front of me but with only one submission left on web assign I remain wary. I still am a bit confused at how to find the velocity with mass, amplitude, max. accel, and 290N/M.

6. Apr 4, 2005

### Hit an Apex

Wow I am stupid!
KE= 1/2 290 N/m * (.026)^2

Thanks!