A block of mass 2,kg is attached to two ident | vedclass

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Question

(A) In this configuration,the two springs are in parallel with respect to the displacement of the block. When the block is displaced by a distance $x$

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) In this configuration,the two springs are in parallel with respect to the displacement of the block. When the block is displaced by a distance $x$,both springs exert a restoring force in the same direction.The effective spring constant $k_{eff}$ for two springs in parallel is given by $k_{eff} = k_1 + k_2$.Given $k_1 = k_2 = 20\,N/m$,we have $k_{eff} = 20 + 20 = 40\,N/m$.The angular frequency $\omega$ of the system is given by $\omega = \sqrt{\frac{k_{eff}}{m}}$.Substituting the values,$\omega = \sqrt{\frac{40}{2}} = \sqrt{20}\,rad/s$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.$T = \frac{2\pi}{\sqrt{20}} = \frac{2\pi}{2\sqrt{5}} = \frac{\pi}{\sqrt{5}}$.Comparing this with the given expression $T = \frac{\pi}{\sqrt{x}}$,we find $x = 5$.

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