A mass '$$\mathrm{m}_1$$' is suspended from a spring of negligible mass. A spring is pulled slightly in downward direction and released, mass performs S.H.M. of period '$$\mathrm{T}_1$$'. If the mass is increased by '$$\mathrm{m}_2$$', the time period becomes '$$\mathrm{T}_2$$'. The ratio $$\frac{\mathrm{m}_2}{\mathrm{~m}_1}$$ is

Two particles $$\mathrm{P}$$ and $$\mathrm{Q}$$ performs S.H.M. of same amplitude and frequency along the same straight line. At a particular instant, maximum distance between two particles is $$\sqrt{2}$$ a. The initial phase difference between them is

$$\left[\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\frac{\pi}{4}\right]$$

A particle of mass 5kg is executing S.H.M. with an amplitude 0.3 m and time period $$\frac{\pi}{5}$$s. The maximum value of the force acting on the particle is

Two bodies $A$ and $B$ of equal mass are suspended from two separate massles springs of force constant $k_1$ and $k_2$, respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body $A$ to that of body $B$ is