All the springs in fig (a), (b) and (c) are identical, each one having force constant K. Mass m is attached to each system. If $T_a$, $T_b$ and $T_c$ are the periodic time of oscillations of the three systems in fig (a), (b) and (c) respectively, then

A particle is performing simple harmonic motion about $x = 0$ with an amplitude '$a$' and periodic time T. The speed of the particle at $x = \dfrac{a}{3}$ will be

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