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

The oscillation of a body on a smooth horizontal surface is represented by the equation, $X=A\cos\,\left(\omega\,t\right)$, where $X=$ displacement at time $t$,$\omega\,=$ frequency of oscillation,$a=$ acceleration at…

A particle is executing SHM along a straight line. Its velocities at distances $x_{1}$ and $x_{2}$ from the mean position are $V_{1}$ and $V_{2}$ respectively. Its time period is:

When two displacements represented by $y_{1}=asin(\omega\,t)$ and $y_{2}=b\cos\,\left(\omega\,t\right)$ are superimposed the motion is:

Two pendulums of length $121\mathrm{cm}$ and $100\mathrm{cm}$ start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum…

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period…

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 =…

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 $n$…

A particle of mass $250g$executes a simple harmonic motion under a periodic force $F=(-25x)N$. The particle attains a maximum speed of $4ms^{-1}$ during its oscillation. The amplitude of the motion is…

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$\pi\,=\frac{22}{7}$]