A particle executes simple harmonic motion with amplitude A and time period 5 s. Starting from the positive extreme position x = A, how much time does it take to reach x = A/√2 for the first time?
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Question

A particle executes simple harmonic motion with amplitude A and time period 5 s. Starting from the positive extreme position x = A, how much time does it take to reach x = A/√2 for the first time?

G1 Physics · Accepted Answer

Choose the SHM equation with the particle starting from the positive extreme: x = A cos(ωt). At the required position, A ÷ √2 = A cos(ωt). Therefore, cos(ωt) = 1 ÷ √2, so for the first time, ωt = π ÷ 4. Since ω = 2π ÷ T, we obtain t = (π ÷ 4) ÷ (2π ÷ T) = T ÷ 8. With T = 5 s, t = 5 ÷ 8 s. Correct option: C.