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The time period of body executing SHM is...

The time period of body executing SHM is 2 seconds. After how much time will its displacement be half of its amplitude ?

Text Solution

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We are given `T=2s,y=(A)/(2)`
As `y=Asinomegat` . . .. (i)
Substituting `y=(A)/(2)" in, (i), we get",(A)/(2)=A sin omegat`
`rArrsin omegat=1/2rArromegat="sin"^(-1)(1)/(2)" or "omegat=pi/6` . . . (ii)
We know that `omega=(2pi)/(T)` . . . (iii)
From (ii) and (iii), we get
`(2pi)/(T)t=(pi)/(6) rArrt=(T)/(12)`
Putting T=2s, we get `t=(2)/(12)=1/6s`
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