The upper end of the spring is fixed and a mass '$$m$$' is attached to its lower end. When mass is slightly pulled down and released, it oscillates with time period 3 second. If mass '$$\mathrm{m}$$' is increased by $$1 \mathrm{~kg}$$, the time period becomes 5 second. The value of '$$\mathrm{m}$$' is (mass of spring is negligible)

For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement '$$x$$' from the mean position. If '$$A$$' is the amplitude of S.H.M the value of '$$x$$' is

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