Showthat the projectionof uniform circular motionon a diameteris SHM.

1.	Showthat the projectionof uniform circular motionon a diameteris SHM.
Answer» <P> Solution :(a) Consider a particlemovingalongthe y cirumferenceof a circleof radius a and centre O,withuniformspeed, v in anticlockwisedirection , LET xx' and yy'be the two perpendicularx diameters. Suppose the particleis at p after a TIME t. If ` omega` is the angularvelcoitythenthe angular displacemetn ` theta`in time t is givenby ` theta = - omega t` From P draw PNperendicularto yy' . As theparticlesmovesfrom X to y , footof the perpendicularN movesfrom 0 to y.As it movesfurther from y to x' , thenfromx' and y' and backagain to x,the POINTN movesfromy to 0 , from 0 to y' and backagainto 0 . Whenthe particle completersone revolution alongthe cirumference, the pointN completersone vibration N alongthe diameter yy' is simpleharmonic. Hence the projection of a unifromcircular motion on a diameterof sidein simple harmonicmotion .

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