The time period of simple harmonic motion of mass $\mathrm{M}$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$, where the value of $\alpha$ is____.
JEE MAIN 2024, Diffcult
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$\mathrm{k}_{\mathrm{eq}}=\frac{2 \mathrm{k} \cdot \mathrm{k}}{3 \mathrm{k}}+\mathrm{k}=\frac{5 \mathrm{k}}{3}$
Angular frequency of oscillation $(\omega)=\sqrt{\frac{\mathrm{k}_{\mathrm{eq}}}{\mathrm{m}}}$
$(\omega)=\sqrt{\frac{5 \mathrm{k}}{3 \mathrm{~m}}}$
Period of oscillation $(\tau)=\frac{2 \pi}{\omega}=2 \pi \sqrt{\frac{3 \mathrm{~m}}{5 \mathrm{k}}}$
$=\pi \sqrt{\frac{12 \mathrm{~m}}{5 \mathrm{k}}}$
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