Question

A simple pendulum  oscillates  in a vertical plane . When it passes through  the mean position, the tension  in the string is 3 times the weight of the pendulum. What is the maximum  displacement  of the pendulum   with respect  to the vertical

Answer 1

T=3mg    (given) at mean position.

For its extreme position lets break its sine and cosine components. sine has no need because we need to find only displacement.

T=3mg(1+cosA)

so,

3mg=3mg(1+cosA)

1=1+cosA

0=cosA

cos90=cosA

A=90

Hence, maximum displacement of the string of the pendulum with respect to the vertical will be at an angle of 90 degree