Oscillations

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

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 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 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…

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…

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

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:

For a simple pendulum, having time period $T$, the variation of kinetic energy (K.E.) with time (t) is represented by :

Match List - I with List - II: [image] Choose the correct answer from the options given below:

A particle is executing a simple harmonic motion. Its maximum acceleration is \$\alpha$ and maximum velocity is \$\beta$. Then, its time period of vibration will be:

The x-t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t=2 s is:[image]

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