Embibe Experts Solutions for Chapter: Simple Harmonic Motion, Exercise 4: Exercise-4

A cylindrical piston of mass $M$ slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of a gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be (process is isothermal)

A U-tube contains mercury of total length $2l$ as shown and is disturbed so that it oscillates back and forth from arm to arm. If we neglect friction, the period of oscillation is:

The time period of a particle in simple harmonic motion is equal to the smallest time between the particle acquiring a particular velocity $\overrightarrow{v}$. The value of $v$ is:

The oscillations represented by curve $1$ in the graph are expressed by equation $x=A\sin \omega t$. The equation for the oscillations represented by curve $2$ is expressed as:

A $4 \mathrm{kg}$ particle is moving along the$x$-axis under the action of the force $F=-\left(\frac{{\pi }^2}{16}\right)x \mathrm{N}$ . At $t=2 \sec$, the particle passes through the origin and at $t=10 \sec$ its speed is $4\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$. The amplitude of the motion is:

Graph shows the$x \left(t\right)$ curves for three experiments involving a particular spring-block system oscillating in SHM. The kinetic energy of the system is largest at $t=4 \mathrm{s}$ for the situation:

The mass and diameter of a planet are twice those of earth. The period of oscillation of the pendulum on this planet will be (If it is the second's pendulum on earth)
 

A uniform rod of length $L$ and mass $M$ are pivoted at the centre. Its two ends are attached to two springs of equal spring constant $k$. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is: