# Simple harmonic motion problem

i need help...

A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 1.0 J of work is required to compress the spring by 0.15 m. If the mass is released from rest with the spring compressed, it experiences a maximum acceleration of 14 m/s^2.

i need to find:
a) The value of the spring constant.
b) The value of the mass.

if any one can help, i would really appreciate it.

quasar987
Homework Helper
Gold Member
Remember that for a mass under the action of a "conservative force" such as the spring force, the change in potential energy is equal to minus the work done on the mass.

Little but important detail: In order to use this fact in your problem, it is necessary to suppose that the mass as been compressed at constant and infinitely small speed, such that we can assert that if the work done by the human force in compressing the mass by 0.15 m is 1.0 J , then the work done by the spring force in compressing the mass by 0.15 m, must be -1.0 J** !

Supposing this condition is met, then the equation

$$\Delta U = - W$$

should be helpful, if you remember that $U_{spring}=\frac{1}{2}kx^2$. As for the part concerning the acceleration, recall how Newton's second law relates force, mass and acceleration.

**You can probably convince yourself of that by considering that under these conditions, the force of spring and the human force differ only in direction, and thus, only is sign!

P.S. You're better off showing us what progress you've made so far in your problems, so we are more able to focus on the points you're having difficulty with.