The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring is cut to half,the same mass oscillates with frequency $v_2$. The value of $v_2/v_1$ is . . . . . . .

Two identical particles each of mass $m$ are interconnected by a light spring of stiffness $k$. The time period for small oscillations is equal to:

The motion of a mass on a spring,with spring constant $K$ is as shown in the figure. The equation of motion is given by $x(t) = A \sin \omega t + B \cos \omega t$ with $\omega = \sqrt{\frac{K}{m}}$. Suppose that at time $t = 0$,the position of the mass is $x(0)$ and velocity is $v(0)$,then its displacement can also be represented as $x(t) = C \cos (\omega t - \phi)$,where $C$ and $\phi$ are:

$A$ solid cylinder of mass $m$ and volume $V$ is suspended from the ceiling by a spring of spring constant $k$. It has a cross-sectional area $A$. It is submerged in a liquid of density $\rho$ up to half its length. If a small block of mass $M_0$ is kept at the center of the top, the amplitude of small oscillation will be:

$A$ mass on a spring oscillates up and down. As the mass moves downward from its highest point to its equilibrium point:

Two particles $A$ and $B$ of masses $m$ and $2m$ are suspended from massless springs of force constants $K_1$ and $K_2$. During their oscillation,if their maximum velocities are equal,then the ratio of amplitudes of $A$ and $B$ is