A rectangular block of mass 'm' and cross-sectional area 'A' floats on a liquid of density '$\varrho$'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency (g=acceleration due to gravity)

For a particle P performing S.H.M., when displacement is 'x', potential energy and restoring force acting on it is denoted by 'E' and 'F' respectively. The relation between x, E and F is

A body of mass $0.4$ kg performs simple harmonic motion. It experiences a restoring force of $0.4$ N when its displacement from the mean position is 4 cm. The force constant and magnitude of acceleration respectively are

The minimum phase difference between two simple harmonic motions is
$x_1 = \dfrac{1}{\sqrt{2}} \sin \omega t + \dfrac{1}{\sqrt{2}} \cos \omega t$
$x_2 = \sin \omega t + \cos \omega t$     $\left[ \sin \dfrac{\pi}{4} = \cos \dfrac{\pi}{4} = \dfrac{1}{\sqrt{2}} \right]$