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The shortest distance travelled by a...

The shortest distance travelled by a particle executing SHM form mean position in 2 seconds is equal to ` ( sqrt(3))/(2 )` times of its amplitude . Determine its time period .

Text Solution

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Given data : `t=2 s , y= ( sqrt(3))/(2) A , T = ?`
displacement ` y=A sin omega t = A sin ( 2pi )/( T ) t`
` ( sqrt(3))/(2) A = A sin"" ( 2 pi xx 2 ) /( t) , sin "" ( 4pi ) /( T) = ( sqrt(3))/(T ) = ( sqrt(3))/(2 ) = sin "" (pi )/(3)`
` therefore ( 4pi )/(T ) = (pi )/(3 ) , T= 12 s`
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