An engine has an efficiency of 1/6. When the temperature of sink is reduced by 62^oC, its efficiency is doubled. Temperatures of the source is

A particle executes simple harmonic oscillation with an amplitude $$a$$. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible.

When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s²).

The particle executing simple harmonic motion has a kinetic energy K₀cos²$$\omega $$t. The maximum values of the potential energy and the total energy are respectively