The time period of a simple pendulum inside a stationary lift is '$$T$$'. When the lift starts accelerating upwards with an acceleration $$\left(\frac{\mathrm{g}}{3}\right)$$, the time period of the pendulum will be

A body is executing a linear S.H.M. Its potential energies at the displacement '$$\mathrm{x}$$' and '$$\mathrm{y}$$' are '$$\mathrm{E}_1$$' and '$$E_2$$' respectively. Its potential energy at displacement $$(\mathrm{x}+\mathrm{y})$$ will be

A simple harmonic progressive wave is represented by $$y=A \sin (100 \pi t+3 x)$$. The distance between two points on the wave at a phase difference of $$\frac{\pi}{3}$$ radian is

The amplitude of a particle executing S.H.M. is $$3 \mathrm{~cm}$$. The displacement at which its kinetic energy will be $$25 \%$$ more than the potential energy is