Chapter 15, Problem 48P

Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = −bv² and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, $E=\frac{1}{2}m{v}^2+\frac{1}{2}k{x}^2$, and use Equation 15.51.