From the figure, obtain the equation of simple harmonic motion of the y-projection of the radius vector of the revolving particle P in each case.

Explanation

In figure, initial phase , `phi_(0)=60^(@)=(pi)/(3)`
radian, amplitude, `a=2cm,T=3s.`
When projection of radius vector is taken on Y-axis, the time for SHM is noted from the mean position.
`:. y=asin(omegat+phi_(0))=asin((2pi)/(T)t +phi_(0))`
`=2sin((2pi)/(3)t+(pi)/(3))`
In fig. ,` phi_(0)=90^(@)=(pi)/(2),`
`a=3m,T=60s`
After time t, it covers an angle `(2pi)/(T)t` in the clockwise direction and makes an angle `((pi)/(2)-(2pit)/(T))` with the x-axis.
`y=3sin((pi)/(2)-(2pit)/(T))=3 cos ((2pit)/(T))`
`=3cos((2pi)/(60))t=3cos((pit)/(30))`