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A particle executes SHM of amplitude 30 ...

A particle executes SHM of amplitude 30 cm and time period 4 second. What is the maximum time required for the particle to move from mean position to a point 15 cm away ?

Text Solution

Verified by Experts

We are given : `A=30" cm",T=4" s and "y=15" cm"`
We are to calculate. Time t
Using relation :
`y=Asinomegat=A "sin"(2pi)/(T)t`
We have, `15=30"sin"(2pi)/(4)t=30"sin"(pi)/(2)t`
`(15)/(30)="sin"(pi)/(2)t,1/2="sin"(pi)/(2)t`
`"sin"^(-1)(1/2)=(pi)/(2)t" or "(pi)/(6)=(pi)/(2)t" or "t=1/3s`
therefore, time required by the particle to move from mean position is `1/3` s
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