# Show the time rate of change of mechanical energy for a damped, undriven oscillator

Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = -bv^2 and hence is always negative. Proceed as follows: Differentiate the expression for the mechanical energy of as oscillator, E = 1/2mv^2 + 1/2kx^2 and use the following equation:

-kx -b dx/dt = m d^2x/dx^2

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