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A block \( A \) of mass \( m \) is placed on a smooth horizontal platform \( P \) and between two elastic massless springs \( S_{1} \) and \( S_{2} \) fixed horizontally to two fixed vertical walls. The elastic constants of the two springs are equal to \( k \) and the equilibrium distance between the two springs both in relaxed states is \( d \). The block is given a velocity \( v_{0} \) initially towards one of the springs and it then oscillates between the springs. The time period \( T \) of oscillations and the minimum separation \( d_{\mathrm{m}} \) of the springs will be
(1) \( T=2\left(\frac{d}{v}+\pi \sqrt{\frac{m}{k}}\right), d_{m}=d \)
(2) \( T=2\left(\frac{d}{v}+2 \pi \sqrt{\frac{m}{k}}\right), d_{m}=d-v \sqrt{\frac{m}{k}} \)
(3) \( T=2\left(\frac{d}{v}+2 \pi \sqrt{\frac{m}{k}}\right), d_{m}=d-2 v \sqrt{\frac{m}{k}} \)
(4) \( T=2 \pi \sqrt{\frac{m}{k}}, d_{m}=d \)
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