A light spring is suspended with mass $$m_1$$ at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is $$T$$ second. When a mass $$m_2$$ is added to $$m_1$$ and the system is made to oscillate, the period is found to be $$\frac{3}{2} T$$. The ratio $$m_1: m_2$$ is

A block of mass '$$M$$' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the piston, is (acceleration due to gravity, $$\mathrm{g}=10 \mathrm{~ms}^{-2}, \pi^2=10$$ )

A simple pendulum of length '$$l$$' and a bob of mass '$$\mathrm{m}$$' is executing S.H.M. of small amplitude '$$A$$'. The maximum tension in the string will be ($$\mathrm{g}=$$ acceleration due to gravity)

The displacement of a particle executing S.H.M. is $$x=\mathrm{a} \sin (\omega t-\phi)$$. Velocity of the particle at time $$\mathrm{t}=\frac{\phi}{\omega}$$ is $$\left(\cos 0^{\circ}=1\right)$$