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Q.

Time period of a particle executing linear S.H.M. is T=4πsec. There is a point P at a distance x = 2 cm from the mean position O. When the particle passes through the point P towards O it has speed v=1cm/sec. The minimum time after which it will again return to point P is

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a

(π/4) sec

b

3π sec

c

(3π/4)sec

d

2πsec

answer is B.

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Detailed Solution

t=T2π(2π−2ϕ)=Tπ(π−ϕ)ϕ=cos-1(xA)=cos-1222ϕ=π/4t=4×3π4=3πsec
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Time period of a particle executing linear S.H.M. is T=4πsec. There is a point P at a distance x = 2 cm from the mean position O. When the particle passes through the point P towards O it has speed v=1cm/sec. The minimum time after which it will again return to point P is