Oscillations and Energy
(1/2)mw2A2cos2(wt+qo) + (1/2)kA2sin2 (wt+qo) .
From the above, it looks like Etotal depends on time. Does this violate Conservation of Energy?
We saw that w = ?(k/m) . Substituting this into the first term gives: Etotal =
(1/2) kA2cos2(wt+qo) + (1/2)kA2sin2 (wt+qo)
= (1/2)kA2 = (1/2) mw2A2, which does NOT depend on time!