A ball is suspended by a thread of length L at the point O on a wall which is inclined to the vertical by α . The thread with the ball is displaced by a small angle β away from the vertical and also a

Question

A ball is suspended by a thread of length L at the point O on a wall which is inclined to the vertical by α . The thread with the ball is displaced by a small angle β away from the vertical and also away from the wall. If the ball is released, the period of oscillation of the pendulum when β > α will be

TestHub · Accepted Answer

θ = θ 0 ​ sin ω t , ω = L g ​ ​ ∵ T = 2 π g L ​ ​ When β > α , time taken by pendulum from B to C and C to B t 1 ​ = 2 T ​ = 2 1 ​ × 2 π g L ​ ​ = π g L ​ ​ Time taken by pendulum from B to A and A to B t 2 ​ = 2 t = ω 2 ​ sin − 1 ( β α ​ ) using θ = θ 0 ​ sin ω t α = β sin ω t or t = ω 1 ​ sin − 1 ( β α ​ ) ∴ Time period of motion T = t 1 ​ + t 2 ​ = g L ​ ​ [ π + 2 sin − 1 β α ​ ]

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