Question

A large block P attached to a light spring executes horizontal, simple harmonic motion as it slides across a frictionless surface with a frequency f = 1.60 Hz. Block B rests on it as shown in the figure, and the coefficient of static friction between the two is Mu_s = 0.510. What maximum amplitude of oscillation can the system have if block B is not to slip cm

Answer 1

when the acceleration of block P exceeds the max possible acceleration of the block B that can be generated by the force of the friction.

using newton's law of motion for block P-

kx = Ma

a = kx/M ...............1

this acceleration must be equal to acceleration produced in block B as -

$\mu$mg = ma

a = $\mu$g ........................2

from equation 1 and 2 -

kx/M = $\mu$g

for maximum amplitude x = a

w = [k/M]^0.5

[2$\pi$*1.60]^0.5 = k/M

k/M = 101.06

101.06 a = 0.510*9.8

a = 0.049 m