A particle executes $SHM.$ Its velocities are $v_1$and $v_2$ at displacement $x_1$ and $x_2$ from mean position respectively. The frequency of oscillation will be
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$\mathrm{V}_{1}=\omega \sqrt{\mathrm{A}^{2}-\mathrm{x}_{1}^{2}}$
$ \Rightarrow \mathrm{V}_{1}^{2}=\omega^{2} \mathrm{A}^{2}-\omega^{2} \mathrm{x}_{1}^{2}$ .......$(1)$
and $V_{2}^{2}=\omega^{2} A^{2}-\omega^{2} x_{2}^{2}$ .........$(2)$
substract eqn $( 2 )$ from $( 1 )$
$\mathrm{V}_{1}^{2}-\mathrm{V}_{2}^{2}=\omega^{2}\left(\mathrm{x}_{2}^{2}-\mathrm{x}_{1}^{2}\right)$
$\omega=\left(\frac{V_{1}^{2}-V_{2}^{2}}{x_{2}^{2}-x_{1}^{2}}\right)^{1 / 2}$
$\mathrm{f}=\frac{1}{2 \pi}\left(\frac{\mathrm{V}_{1}^{2}-\mathrm{V}_{2}^{2}}{\mathrm{x}_{2}^{2}-\mathrm{x}_{1}^{2}}\right)^{1 / 2}$
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