A particle starts oscillating simple harmonically from its mean position with time period \(T\). At time \(t = \frac{T}{6}\), find the ratio of potential energy to kinetic energy of the particle.
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At \(t = T/12\), \(x = A/2\), \(PE/KE = 1/3\). At \(t = T/8\), \(x = A/\sqrt{2}\), \(PE = KE\). At \(t = T/6\), \(x = A\sqrt{3}/2\), \(PE/KE = 3/1\). Memorizing these standard points saves valuable time!