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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