1. Simple harmonic motion (SHM) refers to a special type of oscillations whose restoring force is directly proportional to displacement and acts in the direction opposite to that of displacement.
  • In such oscillations, the displacement-time relationship follows a sinusoidal function x={{x}_{0}}\sin \omega t. E.g.

x={{x}_{0}}\sin \omega t


\begin{array}{l}x={{x}_{0}}\sin \omega t\\\Rightarrow \quad v=\omega x\cos \omega t\\\quad \quad \Rightarrow \quad a=-{{\omega }^{2}}x\sin \omega t\end{array}

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