A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizo

Question

A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u 0 ​ . When the speed of the particle is 0.5 u 0 ​ , it collides elastically with a rigid wall. After this collision :-

TestHub · Accepted Answer

Collision is elastic, so energy is conserved: the particle returns to equilibrium with speed $u_{0}$ (A correct)

$v = ω A^{2} - x^{2}$ with $v = \frac{A ω}{2}$ gives $x = \frac{3 A}{2}$

Time to return first time to equilibrium $= \frac{θ}{ω} = \frac{2 π}{3} \frac{m}{k}$

Option (C) time $= (\frac{2 π}{3} + \frac{π}{2}) \frac{m}{k} = \frac{7 π}{6} \frac{m}{k}$ (wrong)

Option (D) time $= (\frac{2 π}{3} + π) \frac{m}{k} = \frac{5 π}{3} \frac{m}{k}$ (correct)

Answers: (A), (D)

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