# Derive conservation of mechanical energy for a simple spring.

1. Aug 22, 2008

### Narcol2000

Starting with the equation of motion -kx = ma , it is said that integrating this with respect to x gives the equation for conservation of mechanical energy.

Only problem is i don't see how to integrate the right hand side with respect to x...

2. Aug 22, 2008

### tiny-tim

Hi Narcol2000!

Hint: use the Chain Rule to get a as a function of x:

a = dv/dt = (dv/dx)(dx/dt) = … ?

3. Aug 22, 2008

### Narcol2000

Turns into the integral of (mv dv) which gives the answer required... seems so easy looking back.... :(