Question
When will the motion of a simple pendulum be simple harmonic?
✓
Answer
Consider a pendulum of length l and mass of bob m is displaced by angle $\theta$ as shown in fig. 
The restoring force = F $=\text{mg}\sin\theta$ If $\theta$ is small then $\sin\theta=\theta=\frac{\text{arc}}{\text{radius}}=\frac{\text{x}}{\text{l}}$$\therefore\text{F}=-\text{mg}\frac{\text{x}}{1}\ \text{or}\ \text{F}\propto(-\text{x})$
$(\because\text{m}_2\text{g},1\text{are constant})$
Hence, the motion of simple pendulam will be smile harmonic for small angle $\theta.$
The restoring force = F $=\text{mg}\sin\theta$ If $\theta$ is small then $\sin\theta=\theta=\frac{\text{arc}}{\text{radius}}=\frac{\text{x}}{\text{l}}$$\therefore\text{F}=-\text{mg}\frac{\text{x}}{1}\ \text{or}\ \text{F}\propto(-\text{x})$$(\because\text{m}_2\text{g},1\text{are constant})$
Hence, the motion of simple pendulam will be smile harmonic for small angle $\theta.$
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