Oscillations and Energy
(1/2)mw2A2cos2(wt+qo) + (1/2)kA2sin2 (wt+qo) .
Recall that w = ?(k/m) . Thus,
(1/2)mw2A2 = (1/2)kA2 and since sin2q+cos2q=1, we see that Etotal = (1/2)mw2A2 = constant .
Note that the energy of oscillation depends on the frequency squared and the amplitude squared.