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The following figure depicts two circula...

The following figure depicts two circular motions. The radius of the circle, the period of revolutin the initial position and the sense of revolution are indicated on the figure. Obtain the simple harmoic motion of the x-projection of the radius vector of the rotating particle P in each case.

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At t=0 OP makes an angle of `(pi)/2`, with positive x-axis in the clockwise direction. After time t is covers an angle `(2pi)/T t` in the clock wise sense and makes an angle of `(2pi)/Tt+(pi)/2` with positive x-axis. The projection of OP on the axis at time t is given By
`X=Acos ((2pi)/T t+(pi)/2)" "X=-Aisin((2pi)/T t)`
`X=-3sin ((2pi)/2t)" " :. X=-3sinpit`
b.At t=0 OP makes an angle of `pi` with positive x-axis in the anti clockwise direction. After time t is covers an angle `(2pi)/T t` in the anti clock wise sence and makes an angle of `(2pi)/T t+pi` with positive x-axis. The projection of OP on the axis at time t is
`X=Acos((2pi)/T t+pi), " "X=-Acos ((2pi)/T t)`
`x=-2 cos ((2pi)/4t)" "X--2cos ((pi)/2t)`
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