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Question

A particle executes a SHM of time period T. The time taken by the particle to go directly from its mean position to half the amplitude.

A
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Solution

The correct option is A
Let the equation of motion be x=Asinωt
At t = 0, x = 0 Particle is at its mean position.
The particle will be at x=A2 at a time t,
Where A2=Asinωt or sinωt=12 or ωt=π6
(Minimum value of wt is taken because we want to go directly from x = 0 to x=A2 )
Thus, t=π6ω=π6(2πT)=T12

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