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

Two simple pendulums of lengths $L_1$ and $L_2$ have periodic time $T_1$ and $T_2$ respectively $(T_1 > T_2)$. The time period of the pendulum of length $(L_1-L_2)$ is
$[(L_1-L_2) > 60\text{ cm}]$

For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at a certain displacement '$x$' from the mean position. If '$A$' is the amplitude of S.H.M., the value of '$x$' is