A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $$25$$. After how many collisions the amplitude of vibration will become less than $$60$$°

Question

A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $$25$$. After how many collisions the amplitude of vibration will become less than $$60$$°

Infinity Learn · Accepted Answer

From the relation of restitution $$hnh0=e2n$$ and $$hn=h0(1$$−$$cos60$$°$$)$$⇒$$hnh0=1$$−$$cos60$$°$$=252n$$⇒$$1$$−$$12=45n$$⇒$$12=45nTaking$$ log of both sides we get $$log1$$−$$log2=n(log4$$−$$log5)0$$−$$0.3010=n(0.6020$$−$$0.6990)$$− $$0.3010=$$−n×$$0.097$$⇒$$n=0.30100.097=3.1$$≈$$3$$

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A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is 25. After how many collisions the amplitude of vibration will become less than 60°

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