$A$ spring is stretched by $0.20\, m$ when a mass of $0.50\, kg$ is suspended. When a mass of $0.25\, kg$ is suspended,its period of oscillation will be .... $sec$ $(g = 10\, m/s^2)$

$A$ mass is suspended from a vertical spring which is executing $S.H.M.$ of frequency $5 Hz$. The spring is unstretched at the highest point of oscillation. The maximum speed of the mass is [acceleration due to gravity $g=10 m s^{-2}$].

The effective spring constant of the two-spring system as shown in the figure will be:

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 . . . . . . .

$A$ block is fastened to a horizontal spring. The block is pulled to a distance $x = 10 \, cm$ from its equilibrium position (at $x = 0$) on a frictionless surface from rest. The total energy of the block at $x = 5 \, cm$ is $0.25 \, J$. The spring constant of the spring is $......... \, N \, m^{-1}$.

$A$ particle of mass $200 \,g$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N/m$. The time period of oscillations is .... $s$.