Show that for a particle executing SHM described by

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Oscillations · Oscillations

Problem

x(t)=A\cos(\omega t+\phi)

, the kinetic energy as a function of time can be written as

K(t)=\tfrac12 m\omega^{2}A^{2}\sin^{2}(\omega t+\phi)