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Show that simple harmonic motion may be regarded as the projection of uniform circular motion along a diameter of the circle.

Answer» <html><body><p></p>Solution :Tie a ball to the end of a <a href="https://interviewquestions.tuteehub.com/tag/string-11290" style="font-weight:bold;" target="_blank" title="Click to know more about STRING">STRING</a> and make it move in a <a href="https://interviewquestions.tuteehub.com/tag/horizontal-1029056" style="font-weight:bold;" target="_blank" title="Click to know more about HORIZONTAL">HORIZONTAL</a> <a href="https://interviewquestions.tuteehub.com/tag/plane-1155510" style="font-weight:bold;" target="_blank" title="Click to know more about PLANE">PLANE</a> about a fixed point with a constant angular speed. <br/> The ball then perform cirular motion in the horizontal phane. <br/> Observe the motion of ball in a plane by lighting torch in a dark room. The ball will appear to execute to and fro motion along a horizontal line with the point of rotation as the mid-point. Also observe the shadow of the ball on a wall which is perpendicular to the plane of the circle. <br/> Here the motion of the ball on a <a href="https://interviewquestions.tuteehub.com/tag/diameter-950836" style="font-weight:bold;" target="_blank" title="Click to know more about DIAMETER">DIAMETER</a> of the circle normal to the direction of viewing. This is shown in below figure. <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P2_C14_E01_020_S01.png" width="80%"/> <br/> Suppose position of ball moving in circular motion are ABCDEFGA. Observing this plane perpendicularly, the shadow of ball appear on wall will be OPQPORSRO respectively. <br/> The motion of this shadow seems <a href="https://interviewquestions.tuteehub.com/tag/around-5602275" style="font-weight:bold;" target="_blank" title="Click to know more about AROUND">AROUND</a> point O (up and down) which is simple harmonic motion.</body></html>


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