A circular disc of mass $$20 \mathrm{~kg}$$, having radius $$10 \mathrm{~cm}$$ is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The time period of torsional oscillations is found to be $$1 \mathrm{~s}$$. The torsional spring constant of the wire is

A particle executes a simple harmonic motion of amplitude $$\mathrm{A}$$. The distance from the mean position at which its kinetic energy is equal to its potential energy is

The phase difference between displacement and velocity of a particle in simple harmonic motion is

A particle is performing simple harmonic motion. Equation of its motion is $$x = 5\sin \left( {4t - {\pi \over 6}} \right),x$$ being the displacement from mean position. Velocity (in ms$$^{-1}$$) of the particle at the instant when its displacement is 3, will be