Physics - SHM Question with Solution | TestHub

For a particle executing SHM acceleration (a) $\propto -{\omega }^2$ displacement $(x)$ Given $\mathrm{x}=\mathrm{a}{\sin }^2\omega \mathrm{t}$ Differentiating the above equation w.r.t, we get $\frac{\mathrm{dx}}{\mathrm{dt}}=2\mathrm{a}\omega (\sin \omega \mathrm{t})(\cos \omega \mathrm{t})$ Again differentiating, we get $$\begin{array}{rl}& \frac{{\mathrm{d}}^2\mathrm{x}}{{\mathrm{dt}}^2}=\mathrm{a}=2\mathrm{a}{\omega }^2\left[{\cos }^2\omega \mathrm{t}-{\sin }^2\omega \mathrm{t}\right]\\ & =2\mathrm{a}{\omega }^2\cos 2\omega \mathrm{t}\end{array}$$ The given equation does not satisfy the condition for SHM [Eq. (i)] . Therefore, motion is not simple harmonic.