# JEE Main & Advanced Physics Simple Harmonic Motion Differential Equation of S.H.M.

Differential Equation of S.H.M.

Category : JEE Main & Advanced

For S.H.M. (linear) Acceleration $\propto -$ (Displacement)

$A\propto -y$  or $A=-{{\omega }^{2}}y$ or $\frac{{{d}^{2}}y}{d{{t}^{2}}}=-{{\omega }^{2}}y$

or $m\frac{{{d}^{2}}y}{d{{t}^{2}}}+ky=0$        [As  $\omega =\sqrt{\frac{k}{m}}$]

For angular S.H.M. $\tau =-\,c\theta$ and $\frac{{{d}^{2}}\theta }{d{{t}^{2}}}+{{\omega }^{2}}\theta =0$

where ${{\omega }^{2}}=\frac{c}{I}$  [As c = Restoring torque constant and I = Moment of inertia]

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