Derive conservation of mechanical energy for a simple spring.

[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...

 

[tiny-tim]

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...

Hi Narcol2000!

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

a = dv/dt = (dv/dx)(dx/dt) = … ?

 

[Narcol2000]

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

Thanks for your help.