One end of a long metallic wire of length L,a | vedclass

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(D) The metallic wire acts as a spring with an effective spring constant $k_w = \frac{YA}{L}$.The wire and the spring are connected in series.The equi

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$2\pi \sqrt{\frac{m(KL + YA)}{KYA}}$

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(D) The metallic wire acts as a spring with an effective spring constant $k_w = \frac{YA}{L}$.The wire and the spring are connected in series.The equivalent spring constant $k_{eq}$ for two springs in series is given by $\frac{1}{k_{eq}} = \frac{1}{k_w} + \frac{1}{K}$.Substituting $k_w$,we get $\frac{1}{k_{eq}} = \frac{L}{YA} + \frac{1}{K} = \frac{KL + YA}{KYA}$.Thus,$k_{eq} = \frac{KYA}{KL + YA}$.The time period $T$ of a mass-spring system is $T = 2\pi \sqrt{\frac{m}{k_{eq}}}$.Substituting $k_{eq}$,we get $T = 2\pi \sqrt{\frac{m(KL + YA)}{KYA}}$.

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