A particle executes SHM of period 1.2 s and amplitude 8 cm. find the time it takes to travel 3 cm the positive extremity of its oscillation. Given `cos^(-1)(0.625)=51^(@)`.

Explanation

The equation of SHM, when the particle starts swinging from an extreme position, is
`x=acosomegat=acos((2pit)/(T))`
Now x = displacement from mean position
or `x=(8-3)=5cm`
`therefore 5=8cos((2pit)/(T))`
or `cos((2pit)/(T))=(5)/(8)=0.625`
`=cos51^(@)=cos((51xxpi)/(180))`
`therefore (2pit)/(T)=(51xxpi)/(180)`
or `t=(51xxT)/(360)=(51xx1.2)/(360)=0.17sec`