A simple pendulum is oscillating with an amplitude $A$. At what displacement from the mean position is its kinetic energy equal to its potential energy?

If x,v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

A simple pendulum is taken from the equator to the pole. Its period

A disc of radius $R$ and mass $M$ is pivoted at the rim and is set for small oscillations. If simple pendulum has to have the same period as that of the disc, the length of the simple pendulum should be

A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period is given by $T = 2\pi \sqrt {\frac{1}{{g'}}}$ where ${g'}$ is equal to

The length of seconds pendulum on the earth is 1 m. On a planet where the acceleration due to gravity is ${\frac{1}{4}^{th}}$ that on the earth, length of seconds pendulum should be

A mass attached to a spring oscillates horizontally. Its acceleration is $25 \, m/s^2$ when it is 10 cm from its equilibrium position. Find the period of oscillation.

A seconds pendulum at the equator $\left[ {g = 9.8\,\,m/{s^2}} \right]$ is taken to the poles $\left[ {g = 9.83\,\,m/{s^2}} \right]$. If it is to act as second’s pendulum, its length should be

Two simple pendulums, A and B, have lengths $L$ and $4L$ respectively. If the bob of pendulum A is displaced by a small angle $heta$ and released, what angle should the bob of pendulum B be displaced by to have the same maximum velocity as pendulum A?

A planet orbits a star of mass $M$ with an orbital radius $r$. If the star's mass suddenly triples, and the planet's orbital speed remains constant, what would be the planet's new orbital radius?

Two simple harmonic motions are represented by the equations ${y_1} = 0.1\sin \,\,\left( {100\pi t + \frac{\pi }{3}} \right)\,\,{\rm{and}}\,\,{y_2} = 0.1\cos \,\,\pi t.$ The phase difference of the velocity of particle 1, with respect to the velocity of particle 2 is