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For S.H.M., x = A sin(2πt/T). When x = A, A = A sin(2πt/T). When x = A/2, A/2 = A sin(2πt/T). Find t.

1. t = T/4
2. t = T/6
3. t = T/2
4. t = T/12

Correct answer: t = T/6

Solution

For x = A/2, we have A/2 = A sin(2πt/T). Dividing through by A gives 1/2 = sin(2πt/T). The angle whose sine is 1/2 is π/6. Thus, 2πt/T = π/6, which simplifies to t = T/12.

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