$A$ spring is stretched by $0.2 \ m$ when a mass of $0.5 \ kg$ is suspended to it. The time period of the spring when the $0.5 \ kg$ mass is replaced with a mass of $0.25 \ kg$ is (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $s$)

The upper end of the spring is fixed and a mass $m$ is attached to its lower end. When the mass is slightly pulled down and released,it oscillates with a time period of $3 \text{ s}$. If the mass $m$ is increased by $1 \text{ kg}$,the time period becomes $5 \text{ s}$. The value of $m$ is (mass of the spring is negligible).

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:

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

The total spring constant of the system as shown in the figure will be

$A$ 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 ......... $cm$.