A simple pendulum consists of a bob suspended by inextensible and massless thread of length 1 m from a point O. When the bob is at extreme position of oscillation, the thread is suddenly caught by a bolt at a point A located at a distance 0.3 m from O. Now, the bob begins to oscillate in the new condition. Calculate the approximate change in time period of the pendulum. Take, g = 10 ms^(-2).

A simple pendulum consists of a bob suspended by inextensible and mass

1.	A simple pendulum consists of a bob suspended by inextensible and massless thread of length 1 m from a point O. When the bob is at extreme position of oscillation, the thread is suddenly caught by a bolt at a point A located at a distance 0.3 m from O. Now, the bob begins to oscillate in the new condition. Calculate the approximate change in time period of the pendulum. Take, g = 10 ms^(-2).
Answer» Solution :Time period , `T = 2pi sqrt((l)/(g))` As LENGTH,`l = 1 m, T = (2pi)/(sqrt(g))` When the thread is caught by the BOLT at A, the length of the pendulum becomes `l. = 1 - 0.3 = 0.7 m` New time period, `T. = 2pi sqrt((0.7)/(g)) = 2pi sqrt((7)/(10g))` CHANGE in time period, `T = T. = 2pi [(1)/(sqrt(g)) - sqrt((7)/(10g))] = (2pi)/(sqrt(g)) [1-sqrt(0.7)] = 3.162`