Question

In jee till what theta pendulum oscillation consider as SHM

Answer 1

Pendulum oscillations are considered SHM for small angular displacements, typically up to $15^\circ$.

Answer 2

The oscillation of a simple pendulum is approximated as Simple Harmonic Motion (SHM) when the angular displacement from the equilibrium position is small. This is because the restoring force acting on the pendulum bob is given by $F = -mg \sin \theta$, where $m$ is the mass, $g$ is the acceleration due to gravity, and $\theta$ is the angular displacement. For SHM, the restoring force must be directly proportional to the displacement ($F \propto \theta$). For small angular displacements, the trigonometric function $\sin \theta$ can be approximated by $\theta$ itself, provided $\theta$ is measured in radians. Thus, $F \approx -mg \theta$. This linear relationship allows the pendulum's motion to be treated as SHM. The approximation $\sin \theta \approx \theta$ is generally considered valid for angular amplitudes up to about $15^\circ$.