Oscillations

The frequency of small oscillations of thin uniform vertical rod of mass $'m'$ and length $'l'$ hinged at point O with the help of two springs with spring constants $k_1$ and $k_2$, is

The displacement time (x-t) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration fo the particle at $t = 1$ s is

Particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that is at a distance $\dfrac{2A}{3}$ from the equilibrium position. The new amplitude of the motion is

Two SHM's $x_1 = a\sin\left(\omega t + \dfrac{3\pi}{2}\right)$ and $x_2 = a\sin(\omega t + \pi)$ are superimposed on each other. The resultant amplitude of motion is $(\sin \pi/2 = 1$ and $\cos \pi/2 = 0)$

If the length of seconds pendulum on the surface of the earth is 1 m. The length of the seconds pendulum on the surface of the planet is $\left\{g_{planet}=\dfrac{7}{2}g_{earth}\right\}$ {periodic time of the seconds…

A simple pendulum oscillating in air has a period of $\sqrt{3}$ second. If it is immersed in a non-viscous liquid, having density $\rho = \left(\dfrac{1}{x}\right)\sigma$, where $\sigma$ is the density of the material…

The phase of a particle performing a linear S.H.M increases by $\dfrac{\pi^c}{6}$ after every 5 second. The frequency of its oscillation is

The bob of simple pendulum performs S.H.M. with a frequency $'n'$ in air and with frequency $'n_1'$ in water. If the density of the material of bob is $'x'$ g / cc and the ratio $n / n_1$ is 3, then density of bob $'x'$…

There is a large difference between the frequencies of the external periodic force and the natural frequency of a body. The body will

A body of mass $1$ kg is performing linear SHM. Its displacement $x$(cm) at $t$(s) is given by $x=6\sin\left(100t+\dfrac{\pi}{4}\right)$. Maximum kinetic energy of the body 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 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