Exercise-2

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. The amplitude of oscillations of the cage 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:

The amplitude of a particle executing SHM about $O$ is $10\mathrm{cm}$. Then:

The angular frequency of a spring block system is ${\omega }_0$. This system is suspended from the ceiling of an elevator moving downwards with a constant speed $v_0$. The block is at rest relative to the elevator. Lift is suddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement:

The displacement of a particle varies according to the relation $x=3\sin 100t+8{\cos }^{2}50t$. Which of the following is/are correct about this motion.

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.

The displacement-time graph of a particle executing SHM is shown.

Which of the following statements is/are true?