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A simple pendulum of length \( L \) having a bob of mass \( m \) is deflected from its rest position by an angle \( \theta \) and 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 centred at the peg.
(a) Assuming that initially the bob has a height less than the peg, show that the maximum height reached by the bob equals its initial height.
(b) If the pendulum is released with \( \theta=90^{\circ} \) 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 \( \theta=90^{\circ} \).
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