A $2\mathrm{.}00-kg$ block lies at rest on a frictionless table. A spring, with a spring constant of $100\frac{N}{m}$ is attached to the wall and to the block. A second block of $0\mathrm{.}50$ kg is placed on top of the first block. The $2\mathrm{.}00-kg$ block is gently pulled to a position $x=+$A and released from rest. There is a coefficient of friction of $0\mathrm{.}45$ between the two blocks.

a$.$ What is the period of the oscillations?

b$.$ What is the largest amplitude of motion that will allow the blocks to oscillate without the $0\mathrm{.}50-kg$ block sliding off?