It is clear that wave speed ${(v)_{wave}} = v$ and maximum particle velocity
${({v_{\max }})_{particle}} = a\omega = {y_0} \times $ co-efficient of $t = {y_0} \times \frac{{2\pi v}}{\lambda }$
${({v_{\max }})_{particle}} = 2 (\omega)_{wave}$ ==> $\frac{{a \times 2\pi v}}{\lambda } = 2v$ ==> $\lambda = \pi {y_0}$
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$1.$ The net external force acting on the disk when its centre of mass is at displacement $\mathrm{x}$ with respect to its equilibrium position is
$(A)$ $-\mathrm{kx}$ $(B)$ $-2 k x$ $(C)$ $-\frac{2 \mathrm{kx}}{3}$ $(D)$ $-\frac{4 k x}{3}$
$2.$ The centre of mass of the disk undergoes simple harmonic motion with angular frequency $\omega$ equal to
$(A)$ $\sqrt{\frac{k}{M}}$ $(B)$ $\sqrt{\frac{2 \mathrm{k}}{\mathrm{M}}}$ $(C)$ $\sqrt{\frac{2 \mathrm{k}}{3 \mathrm{M}}}$ $(D)$ $\sqrt{\frac{4 \mathrm{k}}{3 \mathrm{M}}}$
$3.$ The maximum value of $\mathrm{V}_0$ for which the disk will roll without slipping is
$(A)$ $\mu g \sqrt{\frac{\mathrm{M}}{\mathrm{k}}}$ $(B)$ $\mu g \sqrt{\frac{M}{2 k}}$ $(C)$ $\mu g \sqrt{\frac{3 M}{k}}$ $(D)$ $\mu g \sqrt{\frac{5 \mathrm{M}}{2 \mathrm{k}}}$
Give the answer question $1,2$ and $3.$