A block $P$ of mass $m$ is placed on a frictionless horizontal surface. Another block $Q$ of same mass is kept on $P$ and connected to the wall with the help of a spring of spring constant $k$ as shown in the figure. $\mu_{s}$ is the coefficient of friction between $P$ and $Q$. The blocks move together performing SHM of amplitude $A$. The maximum value of the friction force between $P$ and $Q$ is 

Since the two blocks move together, they behave like a single system of mass $2m$ attached to a spring of constant $k$. So the angular frequency is $$\omega = \sqrt{\frac{k}{2m}}$$ In SHM, the maximum acceleration is $$a_{\max} = \omega^2 A$$ Thus $$a_{\max} = \frac{k}{2m}A$$ For the upper block $Q$, the only horizontal force is friction. Therefore the friction needed to move it with the common acceleration is maximum when the acceleration is maximum: $$f_{\max} = m a_{\max}$$ Hence $$f_{\max} = m \cdot \frac{kA}{2m}$$ $$f_{\max} = \frac{kA}{2}$$ On checking the options, this matches option $\left(B\right)$.