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(B) The two upper springs are connected in parallel. Their equivalent spring constant is $k_{p} = k + k = 2k$.Now,this equivalent spring is in series

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$2 \pi \sqrt{\frac{3 m}{2 k}}$

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(B) The two upper springs are connected in parallel. Their equivalent spring constant is $k_{p} = k + k = 2k$.Now,this equivalent spring is in series with the third spring of constant $k$. The equivalent spring constant $k_{eq}$ of the system is given by:$\frac{1}{k_{eq}} = \frac{1}{k_{p}} + \frac{1}{k} = \frac{1}{2k} + \frac{1}{k} = \frac{1 + 2}{2k} = \frac{3}{2k}$Therefore,$k_{eq} = \frac{2k}{3}$.The time period $T$ of oscillation for a spring-mass system is given by:$T = 2 \pi \sqrt{\frac{m}{k_{eq}}}$Substituting the value of $k_{eq}$:$T = 2 \pi \sqrt{\frac{m}{2k/3}} = 2 \pi \sqrt{\frac{3m}{2k}}$

$A$ block of mass $m$ hangs from three springs having the same spring constant $k$. If the mass is slightly displaced downwards,the time period of oscillation will be

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