A mass $M$ is performing linear simple harmonic motion, then correct graph for acceleration '$a$' and corresponding linear velocity '$v$' is

A uniform cylinder of mass $m$ and length $l$ having area of cross-section a is suspended lengthwise with the help of a massless spring of constant $k$. The cylinder is half submerged in a liquid of density $\rho$. A small push and release makes it vibrate with small amplitude. The frequency of oscillation is

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of 40 cm. The block just loses contact with the plank when the latter is at momentary rest. Then–

Two block $A$ and $B$ each of mass $m$ are connected by a massless spring of natural length $L$ and spring constant $k$. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown in fig. A third identical block $C$, also of mass $m$, moving on the floor with a speed $v$ along the line joining $A$ and $B$, and collides elastically with $A$. Then