What is the period of small oscillations of t | vedclass

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(A) Let the block of mass $m$ be displaced downwards by a distance $x$.Due to the arrangement of the pulleys and the string,the displacement of the sp

Vedclass · Accepted Answer

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

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(A) Let the block of mass $m$ be displaced downwards by a distance $x$.Due to the arrangement of the pulleys and the string,the displacement of the spring is $4x$.The tension in the spring is $F_s = k(4x) = 4kx$.Since the tension in the string is uniform,the force exerted on the block is $F = 4F_s = 4(4kx) = 16kx$.The restoring force is $F_{restoring} = -16kx$.Comparing this with the standard form $F = -k_{eq}x$,we get $k_{eq} = 16k$.The time period of oscillation is given by $T = 2\pi\sqrt{\frac{m}{k_{eq}}}$.Substituting $k_{eq} = 16k$,we get $T = 2\pi\sqrt{\frac{m}{16k}} = 2\pi \cdot \frac{1}{4} \sqrt{\frac{m}{k}} = \frac{\pi}{2}\sqrt{\frac{m}{k}}$.

What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless?

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