A bar of mass $m$ is suspended horizontally on two vertical springs of spring constant $k$ and $3k$ . The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar (Neglect mass of springs and friction everywhere).
Diffcult
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Let the elongation in spring are $\mathrm{x}_{1} \& \mathrm{x}_{2}$
$x_{1}+x_{2}=2 x$
$3 \mathrm{kx}_{1}=\mathrm{kx}_{2}$
$3 \mathrm{kx}_{1}+\mathrm{kx}_{2}=\mathrm{k}_{\mathrm{eq}} \mathrm{x}$
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}_{\mathrm{eq}}}}$
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