a) When the bob has an initial height less than the peg and then released from rest (figure 1), let body travels from A to B. Since, Total energy at A = Total energy at B,
So, the maximum height reached by the bob is equal to initial height.
b) When the pendulum is released with θ = 90° and x = L/2, (figure 2) the path of the particle is shown in the figure 2. At point C, the string will become slack and so the particle will start making projectile motion. (Refer Q.No. 56)
(1/2)mvc2 – 0 = mg (L/2) (1 – cos θ)
distance between A nd C in the vertical direction is L/2 (1 – cos α)
Again, applying energy principle between A and C,