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(B) Let the block be displaced through a small distance $x$ in the downward direction. Due to this displacement,the string attached to the block stret

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$2\pi \sec 	heta \sqrt {\frac{m}{{2k}}} $

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(B) Let the block be displaced through a small distance $x$ in the downward direction. Due to this displacement,the string attached to the block stretches,causing an elongation $x_1$ in each spring. From the geometry of the setup,the relationship between the downward displacement $x$ and the elongation $x_1$ is given by $x_1 = x \cos 	heta$. The restoring force $F$ acting on the block due to both springs is $F = 2(k x_1) \cos 	heta$. Substituting $x_1 = x \cos 	heta$ into the force equation,we get $F = 2k(x \cos 	heta) \cos 	heta = (2k \cos^2 	heta) x$. Comparing this with the standard restoring force equation $F = k_{eff} x$,the effective spring constant is $k_{eff} = 2k \cos^2 	heta$. The time period $T$ of oscillation is given by $T = 2\pi \sqrt{\frac{m}{k_{eff}}}$. Substituting $k_{eff}$,we get $T = 2\pi \sqrt{\frac{m}{2k \cos^2 	heta}} = 2\pi \sec 	heta \sqrt{\frac{m}{2k}}$.

In the situation as shown in the figure,the time period of vertical oscillation of the block for small displacements will be:

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