Derive conservation of mechanical energy for a simple spring.

AI Thread Summary
The discussion centers on deriving the conservation of mechanical energy from the equation of motion -kx = ma. A participant expresses confusion about integrating the right-hand side with respect to x. Another contributor suggests using the Chain Rule to express acceleration as a function of position, leading to the integral of (mv dv). This approach simplifies the integration process and ultimately provides the necessary derivation for conservation of mechanical energy. The conversation highlights the importance of applying calculus techniques in physics problems.
Narcol2000
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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...
 
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Narcol2000 said:
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! :smile:

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

a = dv/dt = (dv/dx)(dx/dt) = … ? :smile:
 
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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