The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring is cut to one-third,then the same mass oscillates with frequency $v_2$. Then:

Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed supports (see figure). When the mass is displaced from the equilibrium position on either side,it executes simple harmonic motion. The time period of oscillations of this system is ...... .

$A$ block of mass $2\,kg$ is attached to two identical springs,each with a spring constant of $20\,N/m$. The block is placed on a frictionless surface,and the outer ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position,it executes simple harmonic motion. The time period of oscillation is $\frac{\pi}{\sqrt{x}}$ in $SI$ units. The value of $x$ is $..........$

$A$ pan with a set of weights is attached to a light spring. When disturbed,the mass-spring system oscillates with a time period of $0.6 \ s$. When some additional weights are added,the time period becomes $0.7 \ s$. The extension caused by the additional weights is approximately given by ......... $cm$.

$A$ mass '$m_1$' is suspended from a spring of negligible mass. The spring is pulled slightly in the downward direction and released; the mass performs $S.H.M.$ with a period '$T_1$'. If the mass is increased by '$m_2$',the time period becomes '$T_2$'. The ratio $\frac{m_2}{m_1}$ is

On a smooth inclined plane,a mass $M$ is attached between two massless springs of force constant $k$ each,as shown in the figure. The other ends of the springs are fixed to firm supports. The period of oscillation of the mass $M$ is