I got to the point of doing

dv/dt(mv^2-mv0^2) = dv/dt(kx0^2-kx^2)

Is that right? How do I do it?

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- Thread starter lily7
- Start date

I got to the point of doing

dv/dt(mv^2-mv0^2) = dv/dt(kx0^2-kx^2)

Is that right? How do I do it?

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- Dec 30, 2014

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- 11,462

mv^2 -mvo^2 = av^2 - b where a and b are constants. a=m and b = mv0^2.

I am sure you know how to compute the derivative of av^2 wrt t.

The rhs kx0^2-kx^2 = a - bx^2 where a= kx0^2 and b =k.

You need to show some work to get more help.

Ok so then I get 2av=-2bx? And then divide both sides by 2 to get mv=-kx. But, how do I get from there to mdv/dt =-kx?

mv^2 -mvo^2 = av^2 - b where a and b are constants. a=m and b = mv0^2.

I am sure you know how to compute the derivative of av^2 wrt t.

The rhs kx0^2-kx^2 = a - bx^2 where a= kx0^2 and b =k.

You need to show some work to get more help.

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- Aug 27, 2012

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- 1,286

Take the time derivative of both sides:

[imath]\dfrac{1}{2}m \cdot 2 v \dfrac{dv}{dt} = - \dfrac{1}{2}k \cdot 2 x \dfrac{dx}{dt}[/imath]

Hint: What's dx/dt? Is there anything here that will cancel?

-Dan

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- Dec 30, 2014

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You did not take the derivative with respect to t.Ok so then I get 2av=-2bx? And then divide both sides by 2 to get mv=-kx. But, how do I get from there to mdv/dt =-kx?

You should have gotten 2avdv/dt=-2bxdx/dt