Corresponding to two circular motions, the radius of the circle , the period of revolutionthe initial position, and the sense of revolution (i.e. clockwise or anti-clockwise ) are indicated on each figure. Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P. in each case.

Corresponding to two circular motions, the radius of the circle , the

1.	Corresponding to two circular motions, the radius of the circle , the period of revolutionthe initial position, and the sense of revolution (i.e. clockwise or anti-clockwise ) are indicated on each figure. Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P. in each case.
Answer» SOLUTION :a) 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 make an angle of `(2pi)/(T) t + pi/2` with positive x-axis . The projection of OP on the axis at time .t. is given by `X = A cos ((2pi)/(T)t + pi/2) ""X= -A SIN ((2pi)/(T)t)` `X=-3sin ((2pi)/(2)t) ""therefore Z=-3sin pit` 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= A cos ((2pi)/(T)s+ pi) , ""X=-A cos ((2pi)/(T)t)` `X=-2cos ((2pi)/(T)t) , ""X=-2cos((pi)/2 t)`