Kinetic energy of a spring-mass system

[peachy112girl]

Homework Statement

The total energy of a spring-mass system oscillating horizontally is 1600 J. What will be the kinetic energy (in joules) of the mass when its displacement is one-fourth of its amplitude?

Homework Equations

total energy = KE + PE = .5kA²
KE = .5mv²
PE = .5kx²

The Attempt at a Solution

All I have written down is-
1600 J = .5kA²

So, I have no idea how to start solving this problem. Can anyone help me get started? Any help is appreciated!

 

[denverdoc]

At the extreme ends of the displacement, 1/2kx^2=1600 where x is amplitude.

This leads to 1/2k (.25x)^2 = WHAT WE NEED TO KNOW. Set it up as a proportional problem.

AS the total energy is 1600J, the KE will be 1600-PE.