$A$ mass $m$ is suspended separately by two different springs,and the time periods are $t_1$ and $t_2$ respectively. If it is connected by both springs in parallel as shown in the figure,then the time period is $t_0$. The correct relation is:

In a spring-block system as shown in the figure,if the spring constant $K = 9 \pi^2 \ Nm^{-1}$,then the time period of oscillation is (in $s$)

$A$ tray of mass $12 \,kg$ is supported by two identical springs as shown in the figure. When the tray is pressed down slightly and then released, it executes $SHM$ with a time period of $1.5 \,s$. The spring constant of each spring is

$A$ spring of force constant $k$ is cut into two parts whose lengths are in the ratio $1:2$. The two parts are now connected as shown and a block of mass $m$ is connected to the combined spring. Find the period of oscillation performed by the block.

$A$ spring-mass system (mass $m$,spring constant $k$,and natural length $\ell_{0}$) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the center of the disc. If the disc,together with the spring-mass system,rotates about its axis with an angular velocity $\omega$ (where $k >> m \omega^{2}$),the relative change in the length of the spring is best given by which option?

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 the amplitude of $A$ and $B$ is