A small ball is suspended by a thread of length l $$=$$ $$1$$ m at the point O on the wall, forming a small angle α$$=2$$∘ with the vertical (as$$ shown in $$figure). Then the thread with ball was deviated through a small angle β$$=4$$∘ and set free. Assuming the collision of the ball against the wall to be perfectly elastic, the oscillation period of such a pendulum (in$$ $$seconds) is $$___________$$ (Take$$ $$g=$$π$$2).

Question

A small ball is suspended by a thread of length l $$=$$ $$1$$ m at the point O on the wall, forming a small angle α$$=2$$∘ with the vertical (as$$ shown in $$figure). Then the thread with ball was deviated through a small angle β$$=4$$∘ and set free. Assuming the collision of the ball against the wall to be perfectly elastic, the oscillation period of such a pendulum (in$$ $$seconds) is $$___________$$ (Take$$ $$g=$$π$$2).

Infinity Learn · Accepted Answer

The time period of free, oscillation of pendulum $$T=2$$$$π$$$$lg=2sTime$$ taken by bob to go from extreme position A to mean position B is $$=T4Time$$ taken by bob to move from mean position B to position C (where$$ its angular displacement α is half the angular amplitude β$$) is found from equation α$$=$$β$$sin$$⁡$$2$$$$π$$Tt.Solving we get $$t=T12$$⇒ Total time period of $$oscillation=2T4+T12=23T=43s$$

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