If two similar springs each of spring constant $K$ are joined in series,the new spring constant and time period would be changed by a factor of:

$A$ block of mass $1 \; kg$ is fastened to a spring with a spring constant of $50 \; N m^{-1}$. The block is pulled to a distance $x = 10 \; cm$ from its equilibrium position at $x = 0$ on a frictionless surface and released from rest at $t = 0$. Calculate the kinetic,potential,and total energies of the block when it is $5 \; cm$ away from the mean position.

$A$ spring of unstretched length $l$ has a mass $m$ with one end fixed to a rigid support. Assuming the spring to be made of a uniform wire,the kinetic energy possessed by it if its free end is pulled with uniform velocity $v$ is

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

$A$ mass $m$ is suspended by means of two coiled springs which have the same length in the unstretched condition,as shown in the figure. Their force constants are $k_1$ and $k_2$ respectively. When set into vertical vibrations,the period will be:

$A$ particle of mass $m$ in a unidirectional potential field has potential energy $U(x) = \alpha + 2 \beta x^2$,where $\alpha$ and $\beta$ are positive constants. Find its time period of oscillation.