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.

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. To do so, differentiate the expression for the mechanical energy of an oscillator, E = 1/2mv^2 + 1/2kx^2