First slide

Simple hormonic motion

Question

A simple pendulum of length / and bob mass m is displaced from its equilibrium position O to a position P so that the height of P above O is h, It is then released. What is the tension in the string when the bob passes through the equilibrium position O ? Neglect friction, v is the velocity of the bob at O.

Easy

A

$mgh / l$
B

$2 mgh / l$
C

$mg(1+h/l)$
D

$mg (1 + 2 h / l)$

Solution

The velocity v at equilibrium position O when released from position P is given by
$\frac{1}{2} {mv}^{2} = mgh or v^{2} = 2 gh At O, let the tension in the string be T . Then T - mg = {mv}^{2} / l T = mg + ({mv}^{2} / l) = mg + (\frac{2 mgh}{l}) = mg (1 + \frac{2 h}{l})$

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