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4) When a mass of 1 kg is suspended from a vertical spring. Its length increases by 0.98 m. If this mass is pulled downwards and then released, what will be periodic time of vibration of spring? (g = 9.8 m/s2 )

5) A block of mass 'm' moving with velocity (v) collides perfectly inelastically with another identical block attached to spring of force constant K. What will be the amplitude of resulting SHM?

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5 ans) Collision is perfectly elastic. So, after collision both bodies stick together and moves with velocity V’ So, initial linear momentum = final linear momentum mv = ( m + m)v’ v’ = v/2 Now, potential energy stored in spring = kinetic energy after collision of bodies ⇒ 1/2 kx² = 1/2 (2m)v²/4 ⇒ x² = mv²/2k ⇒x = v√(m/2k) Regards.
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