Which physical quantity remains conserved in Simple Harmonic Motion
Answers
Simple harmonic motion is normally treated as friction-free, or having zero dissipation. Thus the total energy (E) is constant, with the division of E between kinetic (T) and potential (V) varying in a sinusoidal manner from 0% to 100% for each. Another way to describe it is that the time-averaged values of both the system’s Lagrangian (L = T - V) and Hamiltonian (H = T + V) are constant, the former at zero and the latter at E. The cycling between T and V occurs at the natural frequency of f = sqrt(K/m)/2pi, K being the restoring force and m the effective mass. For a mass attached to a spring, K is just the spring stiffness; for a pendulum of length l with the mass attached to the end, K is close to mg/l for small amplitudes, but for large amplitudes no analytic solution exists so f must be approximated numerically. And of course if any sources of friction are present the oscillatory motion will gradually dampen out and cease.