A simple pendulum of length L having a bob of mass m is deflected from its rest position by an angle 6 arid released (figure 8-E16). The string hits a peg which is fixed at a distance x below the point of suspension and the bob starts going in a circle centered at the peg.

(a) Assuming that initially the bob has a height less that the peg, show that the maximum height reached by the bob equals its initial height,

(b) If the pendulum is released with θ = 90° and x = L/ 2 find the maximum height reached by the bob above its lowest position before the string becomes slack,

(c) Find the minimum value of x/L for which the bob goes in a complete circle about the peg when the pendulum is released from θ = 90°.