Answer:
Fm = μ M g maximum force that can be applied to object with object not slipping
F = M * ω^2 A since ω^2 A is the maximum acceleration of SHM
μ M g = M * ω^2 A equating forces
A = μ g / ω^2 = μ g / (2 π f)^2
A = .55 * 9.80 m/s^2/ (6.28 * 2.10 / s)^2 = .031 m