Answer the following questions:The motion of a simple pendulum is… - Vidyadip

Question

Answer the following questions:The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than $2\pi\sqrt{\frac{\text{l}}{\text{g}}}.$ Think of a qualitative argument to appreciate this result.

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Answer

In the case of a simple pendulum, the restoring force acting on the bob of the pendulum is given as:$\text{F}=-\text{mg}\sin\theta$
Where, F = Restoring force m = Mass of the bob g = Acceleration due to gravity$\theta=$ Angle of displacement
For small $\theta,\ \sin\theta\simeq\theta$ For large $\theta,\ \sin\theta$ is greater than $\theta.$ This decreases the effective value of g. Hence, the time period increases as: $\text{T}=2\pi\sqrt{\frac{\text{l}}{\text{g}}}$ Where, l is the length of the simple pendulum.

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