Starting from the origin a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy?

1/6 s
1/4 s
1/3 s
1/12 s

Correct answer: 1/6 s

Solution

KE is 75% of total when PE is 25%, i.e. x = A/2. Starting from the mean position x = A sin(wt), so sin(wt)=1/2, wt = pi/6. With w = 2*pi/T = pi, t = (pi/6)/pi = 1/6 s.

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