The angular frequency of the simple harmonic motion is ω. The coefficient of friction between the coin and the platform is μ.

Question

A coin is placed on a horizontal platform, which undergoes horizontal simple harmonic motion about a mean position O. The coin does not slip on the platform. the angular frequency of the simple harmonic motion is ω. The coefficient of friction between the coin and the platform is μ. The amplitude of oscillation is gradually increased. The coin will begin to slip on the platform for the first time

(a) at the extreme positions of oscillations 

(b) at the mean position

(c) for an amplitude of μg/ω²

(d) for an amplitude of g/μω²

Answer 1

Correct Answer is: (a, c)

Let O be the mean position and x be the displacement from the mean position. 

Acceleration = a = ω² x.

If F = the force of friction, F = ma = mω²x.

The coin will slip when F = F_lim = μN = μmg.

Let amplitude = x_max = A.

∴ μmg = mω² A  or A = μg/ω².