Oscillations

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude…

The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure. $y$-projection of the radius vector of rotating particle $P$ is

A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period $T_{1}$ and (ii) back and forth in a direction perpendicular to its plane, with a period$T_{2}$. The…

A particle executes simple harmonic motion between $x=-A\text{and}x=+A$. If time taken by particle to go from $x=0$ to $\frac{A}{2}$ is $2s$; then time taken by particle in going from$x=\frac{A}{2}$to $A$is:

Two identical tennis balls each having mass $m$and charge $q$are suspended from a fixed point by threads of length $l.$ What is the equilibrium separation when each thread makes a small angle $\theta\,$ with the…

A particle executes S.H.M. of amplitude $A$along $x$-axis. At $t=0$, the position of the particle is $x=\frac{A}{2}$ and it moves along positive $x$-axis. The displacement of particle in time $t$ is…

Match List-I with List-II. List-IList-IIA. $\sin^2 \omega t$I. Periodic with time period $T = \dfrac{\pi}{\omega}$ but not simple harmonic motion (SHM)B. $\sin^3(2\omega t)$II. Periodic with time period $T =…

The velocity of a particle executing SHM varies with displacement ($x$) as $4v^{2}=50-x^{2}$. The time period of oscillations is$\frac{x}{7}s$. The value of $x$ is ______. [Take$\pi\,=\frac{22}{7}$]

A particle executes simple harmonic motion with an amplitude of $4\mathrm{cm}$. At the mean position, velocity of the particle is $10\mathrm{cm}s^{-1}$. The distance of the particle from the mean position when its speed…

A particle performs simple harmonic motion with amplitude $A$. Its speed is increased to three times at an instant when its displacement is$\frac{2A}{3}$.The newamplitude of motion is$\frac{nA}{3}$.The value of $n$…

The velocity of a particle executing simple harmonic motion along $x$-axis is described as $v^2 = 50 - x^2$, where $x$ represents displacement. If the time period of motion is $\dfrac{x}{7}$ s, the value of $x$ is _____?

A particle executes simple harmonic motion represented by displacement function as$x(t)=A\sin\,(\omega\,t+\varphi\,)$.If the position and velocity of the particle at $t=0s$ are $2\mathrm{cm}$ and…