A particle is executing simple harmonic motion with an instantaneous displacement $$x=A \sin ^2\left(\omega t-\frac{\pi}{4}\right)$$. The time period of oscillation of the particle is

If the amplitude of a lightly damped oscillator decreases by $$1.5 \%$$ then the mechanical energy of the oscillator lost in each cycle is

A body is executing S.H.M. At a displacement $$x$$ its potential energy is 9 J and at a displacement $$y$$ its potential energy is 16 J . The potential energy at displacement $$(x+y)$$ is

A hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density $$\rho$$. If the mass of hydrometer is $$m$$ and the radius of the hydrometer tube is $$r$$, then the time period of oscillation is