Simple Harmonic Motion 4 Question 12

12. A particle of mass m is attached to one end of a massless 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 u0. When the speed of the particle is 0.5u0, it collides elastically with a rigid wall. After this collision

(2013 Adv.)

(a) the speed of the particle when it returns to its equilibrium position is u0

(b) the time at which the particle passes through the equilibrium position for the first time is t=πmk

(c) the time at which the maximum compression of the spring occurs is t=4π3mk

(d) the time at which the particle passes through the equilibrium position for the second time is t=5π3mk

Numerical Value

Show Answer

Answer:

Correct Answer: 12. (a, d)

Solution:

  1. At equilibrium (t=0) particle has maximum velocity u0. Therefore velocity at time t can be written as

writing, u=umaxcosωt+u0cosω

ωt=π32πTt=π3t=T6

(b) t=tAB+tBA=T6+T6=T3=2π3mk

(c) t=tAB+tBA+tAC=T6+T6+T4=712T=7π6mk

(d) t=tAB+tBA+tAC+tCA=t6+T6+T4+T4=56T

=5π3mk



NCERT Chapter Video Solution

Dual Pane