Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Oscillations, Exercise 4: Evaluation Test

A plank with a small block on top of it is undergoing SHM in vertical direction of period $2 \mathrm{s}$. The minimum amplitude at which block will separate from the plank is:

An ideal gas is kept in a cylinder of cross-sectional area $A$ and volume $V_0.$ The mass of the gas enclosed is $M$ and bulk modulus$B$. If the piston of the cylinder is pressed by a small distance $x$, then find the time period of small oscillations.

Consider a sphere of radius  $r$ rolling on a hemispherical surface of radius $R$. When the ball is at the bottom-most point, it is slightly displaced and released. Find its time period for small oscillations, if $r=0.5 \mathrm{m}$, and $R=5 \mathrm{m}$.

A cart of mass $M$ that can slide on frictionless rails has a pendulum bob of mass $m$ connected to it through a massless inextensible string. The cart can move only longitudinally on the rails. The ratio of time periods $\left(\frac{T_2}{T_1}\right)$, when the pendulum swings in the vertical planes parallel and perpendicular to the rails is

Assuming all the surfaces to be smooth, find the time period of oscillation of the ball released from the top of the wedge.

A box placed on a smooth inclined plane is free to move. Find the time period of oscillation of the simple pendulum attached to the ceiling of the box.

A ball suspended by a thread of length $L$ at a point $O$ on the wall forms a small angle $\alpha$ with the vertical. Then, the thread with the ball is deviated through a small angle $\beta >\alpha$ and set free. Assuming the collision of the ball with the wall as elastic, find the time period of oscillation of such a pendulum.

In case of a mechanical wave, a particle oscillates, During oscillation, its kinetic and potential energy changes.  When particle is passing through mean position,