A block A of mass 1, kg is connected to two i | vedclass

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Question

(A) When the block $A$ is displaced by a small distance $x$ to the left,the left spring is compressed by $x$ and the right spring is stretched by $x$.

Vedclass · Accepted Answer

$\frac{\pi}{20}\,s$

Vedclass · Answer

(A) When the block $A$ is displaced by a small distance $x$ to the left,the left spring is compressed by $x$ and the right spring is stretched by $x$.Both springs exert a restoring force towards the equilibrium position.The total restoring force is $F = -k x - k x = -2k x$.Comparing this with the standard equation for simple harmonic motion $F = -k_{eff} x$,we get the effective spring constant $k_{eff} = 2k$.Given $m = 1\, kg$ and $k = 800\, N/m$,the effective spring constant is $k_{eff} = 2 	imes 800 = 1600\, N/m$.The time period $T$ of the oscillation is given by $T = 2\pi \sqrt{\frac{m}{k_{eff}}}$.Substituting the values,$T = 2\pi \sqrt{\frac{1}{1600}} = 2\pi 	imes \frac{1}{40} = \frac{\pi}{20}\,s$.

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