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

A ball is suspended by a thread of length $L$ at the point $O$ on the wall $PQ$ which is inclined to the vertical through an angle $\alpha$. The thread with the ball is now displaced through a small angle $\beta$ away from the vertical and the wall. If $\beta <\alpha$, then the time period of oscillation of the pendulum will be

A cage of mass $M$ hangs from a light spring of force constant $k$. A body of mass $m$ falls from height $h$ inside the cage and sticks to its floor. 

In the above problem, the frequency of oscillations of the cage will be:

Two blocks of masses $3\mathrm{kg}$ and $6\mathrm{kg}$ rest on a horizontal smooth surface. The $3\mathrm{kg}$ block is attached to a spring with a force constant $k=900{\mathrm{Nm}}^{-1}$ which is compressed $2\mathrm{m}$ from beyond the equilibrium position. The $6\mathrm{kg}$ block is at rest at $1\mathrm{m}$ from mean position. $3\mathrm{kg}$ mass strikes the $6\mathrm{kg}$ mass and the two stick together.