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Question

# A particle executes SHM with a time period of 8 s. Find the time taken by the particle to go directly from its mean position to half of its amplitude.

A
13 s
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B
23 s
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C
2 s
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D
1 s
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Solution

## The correct option is B 23 sIf the particle starts from the mean position in positive direction, then equation of motion can be given by x=Asin(ωt) By given condition, A2=Asin(ωt) ⇒ ωt=sin−1(12)=π6 ⇒ t=π6ω Given, T=2πω=8 s ⇒ ω=π4 rad/s Putting the value of ω ∴ t=π6×4π=23 s Why this question? Tips: A particle executing SHM covers first A2 distance in t s and second A2 distance in 2t s, when particle start from mean position.

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