A simple pendulum has a length L and a bob of mass m. The bob is oscillating with amplitude A. Show that the maximum tension (T) in the string is (for small angular displacement). T_("max") =mg [1+(A/L)^(2)].

A simple pendulum has a length L and a bob of mass m. The bob is oscil

1.	A simple pendulum has a length L and a bob of mass m. The bob is oscillating with amplitude A. Show that the maximum tension (T) in the string is (for small angular displacement). T_("max") =mg [1+(A/L)^(2)].
Answer» Solution :Here, Mass of bob =m,Amplitude of oscillation = A, Length of PENDULUM = L, `/_BAC = THETA` Tension `T= mg cos theta +(mv^2)/(L)""[(mv^(2))/(L) = " centripetal force "]` If `cos theta =1` `v= v_("max") " and " T= T_("max")` `T_("max") = mg +(mv_("max")^(2))/(L)"""..........."(1)` `=mg +(mA^(2)omega^(2))/(L)" but "omega^(2) = (g)/(L)` `T_("max") = mg+ (mA^(2) g)/(L xx L)""".........."(2)` `THEREFORE T_("max") = mg +(mgA^(2))/(L^2)` `therefore T_("max") = mg[1+(A/L)^(2)]`.