$A$ force of $6.4 \ N$ stretches a vertical spring by $0.1 \ m$. The mass that must be suspended from the spring so that it oscillates with a time period of $\pi/4 \ s$ is .... $kg$.

$A$ $2\, kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi^2\, N/m$ attached to a $2\, kg$ block at rest kept on a smooth floor. The time for which the moving block remains in contact with the spring will be ... $\sec$.

Two springs of constant $k_1$ and $k_2$ are joined in series. The effective spring constant of the combination is given by

In the adjacent figure,if the inclined plane is smooth and the springs are identical,then the period of oscillation of this body is

In the arrangement given in the figure,if the block of mass $m$ is displaced,the frequency is given by:

Two massless springs of force constants $K_1$ and $K_2$ are joined end to end. The resultant force constant $K$ of the system is