Answer to Question #253165 in Mechanics | Relativity for Tithi

Question

Show that the average rate of energy dissipation is equal to the work done by the damping for per second.

Answer 1

For a system that has a small amount of damping, the period and frequency are nearly the same as for simple harmonic motion, but the amplitude gradually decreases. This occurs because the non-conservative damping force removes energy from the system, usually in the form of thermal energy. In general, energy removal by non-conservative forces is described as W_nc = Δ(KE + PE), where W_nc is work done by a non-conservative force (here the damping force). For a damped harmonic oscillator, W_nc is negative because it removes mechanical energy (KE + PE) from the system.