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Show that the projection of uniform circular motion on a diameter is SHM. |
Answer» Solution :considera particle moving along the y circumference of a circle of RADIUS a andcentre O , with uniform speed V, in anticlockwise direction  Let xx' and yy' be the two perpendicular x diameters . Suppose the particle is at p after a TIME t. If `SQUARE` is the angular velocity then the angular displacement `theta` in time t is given by `theta=-square t.` From P draw PN perpendicular to yy'. AS the particles moves from x to y , foot of the perpendicular N moves from 0 to y . As it moves further from y to x', then from x' to y' and back again to x, the point N moves from y to 0 , from 0 to y' and back again to 0 . When the particle CONFERENCE , the point N completes one vibration about the mean position 0 . The motion of the point N along the diameter yy' is simple harmonic. Hence the projection of a uniform circular motion on a diameter of side in simple harmonic motion. |
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