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1. The problem statement, all variables and given/known data

I simply need to show that the rate of energy for a damped oscillator is given by:

dE / dT = -bv^2, where b is the dampening coefficient

2. Relevant equations

I am instructed to differentiate the formula:

E = 1/2 mv[tex]^{2}[/tex] + 1/2 kx[tex]^{2}[/tex] (1)

and use the formula: -kx - b dx/dt = m d[tex]^{2}[/tex]x/dt[tex]^{2}[/tex] (2)

3. The attempt at a solution

I differentitiate

E = 1/2 mv[tex]^{2}[/tex] + 1/2 kx[tex]^{2}[/tex]

to get dE/dT = m d[tex]^{2}[/tex]x/dt[tex]^{2}[/tex] + k dx/dt

the only thing I can see to do here is sub in the above formula (2), to get

dE / dt = -kx - b dx/dt + k dx/dt

or

dT / dt = -kx - bv + kv

I must be missing something here, or maybe I made a mistake somewhere, but this question has been bugging me since yesterday. If anyone could steer me in the right direction I would definitely appreciate it.

Thanks alot

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# Homework Help: Energy of a damped oscillator

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