A simple pendulum is vibrating with an angular amplitude of 90^(@) as shown in the figure. For what value of a is the acceleration directed i) vertically upwards ii) horizontally iii) vertically downward

A simple pendulum is vibrating with an angular amplitude of 90^(@) as

1.	A simple pendulum is vibrating with an angular amplitude of 90^(@) as shown in the figure. For what value of a is the acceleration directed i) vertically upwards ii) horizontally iii) vertically downward
Answer» `0^(@), cos^(-1)(1/sqrt3), 90^(@)` `90^(@), cos^(-1)(1/sqrt3), 0^(@)` ` cos^(-1)(1/sqrt3),0^(@), 90^(@)` ` cos^(-1)(1/sqrt3),90^(@), 0^(@)` SOLUTION : At "C", `T cos alpha = MG .......(i)` `P.E_(B) = K.E_(A) Rightarrow mgr = 1/2(mv_(A)^(2))` hence at "C" , `v = SQRT (v_(A)^(2) - 2gr(1-cos alpha))` `T -Mg cos alpha = (Mv)^(2)/(r) = (M.2 GR cos alpha)/(r)`