The displacement of a particle performing linear S.H.M. is given by $y = A\cos[\pi(t + \phi)]$. If at $t = 0$, the displacement is $y = 2$ cm and velocity is $2\pi$ cm/s, the value of amplitude A in cm is

A light spring is suspended with mass '$m_1$' at its lower end and its upper end is 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 $\dfrac{3}{2}$ T. The ratio $\left(\dfrac{m_1}{m_2}\right)$ is

For a particle performing linear S.H.M. of amplitude 'r', the potential energy is '$\lambda$' times its total energy. The displacement of particle is

In a sonometer experiment, the fundamental frequency of vibration of wire is '$n_1$' when wire is stretched by hanging a metal bob. If the bob is completely immersed in water, the frequency of vibration of wire becomes '$n_2$'. The relative density of the metal of the bob is