The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

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12 s

36 s

8 s

6 s

answer is D.

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Detailed Solution

$X = A \sin ω t (t = 3, X = \frac{A}{2}) \Rightarrow \frac{A}{2} = A \sin 3 ω \Rightarrow \sin 3 ω = \frac{1}{2} \Rightarrow 3 ω = \frac{π}{6} \Rightarrow ω = \frac{π}{18} = \frac{2 π}{T} \Rightarrow T = 36 s$

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