Oscillations question bank (Physics)

Two blocks of masses $m$ and $M,(M \gt m)$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
($\mu=$ coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is $\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}$
(B) The acceleration of the blocks is $\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}$ ($\mathrm{x}=$ displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is $\frac{m \mu|x|}{M+m}$
(D) The maximum amplitude of the upper block, if it does not slip, is $\frac{\mu(M+m) g}{k}$
(E) Maximum frictional force can be $\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}$.
Choose the correct answer from the options given below:

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y \pi \times 10^{-2} \mathrm{~s}$, where the value of $y$ is (Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$, density of water $=10^3 \mathrm{~kg} / \mathrm{m}^3$ )