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Derive conservation of mechanical energy for a simple spring.

  1. Aug 22, 2008 #1
    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. jcsd
  3. Aug 22, 2008 #2


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    Hi Narcol2000! :smile:

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

    a = dv/dt = (dv/dx)(dx/dt) = … ? :smile:
  4. Aug 22, 2008 #3
    Turns into the integral of (mv dv) which gives the answer required... seems so easy looking back.... :(

    Thanks for your help.
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