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Assuming all pulleys, springs and string massless. Consider all surface smooth. Choose the correct statement $(s)$
The angular frequency for small oscillation of the system is $\sqrt \frac{K}{3m}$
The angular frequency for small oscillation of the system is $\sqrt \frac{4K}{33m}$
The elastic potential energy of system at equilibrium is $\frac{33m^2g^2}{4K}$
The elastic potential energy of system at equilibrium is $\frac{3m^2g^2}{2K}$
Solution
$x=\frac{y_{1}}{2}+2 y_{2}+2 y_{3}$ $…(1)$
$\Delta \mathrm{T}=\mathrm{ma}$ $…(2)$
$2 \Delta \mathrm{T}=\mathrm{Ky}_{2}$ $…(3)$
$2 \Delta \mathrm{T}=\mathrm{Ky}_{3}$ $…(4)$
$\frac{\Delta \mathrm{T}}{2}=\mathrm{Ky}_{1}$ $…(5)$
Solving eqn.
$x=\Delta T\left(\frac{33}{4 K}\right)$
$w^{2}=\left(\frac{4 K}{33}\right)$
