### A spring of spring constant k sits on a frictionless horizontal surface, one end of the spring is attached to a wall, the other end to a block of

A spring of spring constant k sits on a frictionless horizontal surface, one end of the spring is attached to a wall, the other end to a block of mass M, also resting on the frictionless surface. The system executes simple harmonic motion such that at a given point the mass is -1/6 of the amplitude moving away from equilibrium, and 0.5 seconds later it has 1/7 of the maximum speeds, moving towards equilibrium, having passed equilibrium once.

(a) Find the period of the motion

(b) The system is brought to rest at equilibrium, and a block of mass m=M/2 collides in-elastically with the block attached to the spring, if M is 1.2 kg, find the amplitude of the resulting motion.

(c)

What must be the coefficient of static friction between a block of mass M/4, resting on top of the block of mass M, while M is still attached to the block of mass M/2, and M, so that the smaller block is on the verge of slipping at maximum acceleration?

My question is on part(c), when calculating mu using the amplitude, is it the same as what we calculated in part (b)? Why?

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