$A$ 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 $T$ seconds. 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

In the given figure,a body of mass $M$ is held between two massless springs on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has a spring constant $k,$ the frequency of oscillation of the given body is:

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2$,respectively. If the maximum velocities during oscillations are equal,the ratio of amplitudes of $A$ and $B$ is

$A$ small block of mass $m$,having charge $q$,is placed on a frictionless inclined plane making an angle $\theta$ with the horizontal. There exists a uniform magnetic field $B$ parallel to the inclined plane but perpendicular to the length of the spring. If $m$ is slightly pulled on the inclined plane in the downward direction and released,the time period of oscillation will be (assume that the block does not leave contact with the plane):

$A$ spring with a spring constant of $1200\, Nm^{-1}$ is mounted on a smooth frictionless surface and attached to a block of mass $3\, kg$. The block is pulled $2\, cm$ to the right and released. The angular frequency of oscillation is .... $rad/s$.

$A$ particle of mass $200 \,g$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N/m$. The time period of oscillations is .... $s$.