Find the ratio of time periods of two identical springs if they are first joined in series and then in parallel and a mass $m$ is suspended from them.

$A$ bar of mass $m$ is suspended horizontally on two vertical springs of spring constant $k$ and $3k$. The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar (Neglect mass of springs and friction everywhere).

$A$ block of mass $1 \ kg$ is fastened to a spring of spring constant $100 \ N \ m^{-1}$. The block is pulled to a distance $x = 10 \ cm$ from its equilibrium position $(x = 0 \ cm)$ on a frictionless surface,from rest at $t = 0$. The kinetic energy and the potential energy of the block when it is $5 \ cm$ away from the mean position are:

One end of a long metallic wire of length $L$ is tied to the ceiling. The other end is tied to a massless spring of spring constant $K$. $A$ mass $m$ hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire are $A$ and $Y$ respectively. If the mass is slightly pulled down and released,it will oscillate with a time period $T$ equal to

$A$ $2\, kg$ 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 ... $\sec$.

When a mass $m$ is attached to a spring,it extends by $0.2 \ m$. The mass $m$ is given a slight additional extension and released. Find the time period (take $g = \pi^2 \ m/s^2$).