Three masses $500 \ g$,$300 \ g$,and $100 \ g$ are suspended at the end of a spring as shown in the figure and are in equilibrium. When the $500 \ g$ mass is removed,the system oscillates with a period of $2 \ s$. When the $300 \ g$ mass is also removed,it will oscillate with a period of (in $s$)

$A$ $3 \ kg$ block is connected as shown in the figure. The spring constants of the two springs $K_1$ and $K_2$ are $50 \ Nm^{-1}$ and $150 \ Nm^{-1}$ respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is $(g=10 \ ms^{-2})$. (in $ms^{-2}$)

$A$ mass $m$ performs oscillations of period $T$ when suspended by a spring of force constant $K$. If the spring is cut into two equal parts and arranged in parallel,and the same mass $m$ is oscillated by them,then the new time period will be:

$A$ spring stretches by $2 \text{ mm}$ when it is loaded with a mass of $200 \text{ g}$. From the equilibrium position,the mass is further pulled down by $2 \text{ mm}$ and released. The frequency associated with the system and the maximum energy in the spring are . . . . . . $\text{Hz}$ and . . . . . . $\text{J}$,respectively. (Take $g = 10 \text{ m/s}^2$)

In figure $(A)$,mass '$2m$' is fixed on mass '$m$' which is attached to two springs of spring constant $k$. In figure $(B)$,mass '$m$' is attached to two springs of spring constant '$k$' and '$2k$'. If mass '$m$' in $(A)$ and $(B)$ are displaced by distance '$x$' horizontally and then released,then the time periods $T_{1}$ and $T_{2}$ corresponding to $(A)$ and $(B)$ respectively follow the relation.

$A$ vertical spring oscillates with a period of $6 \ s$ when a mass $m$ is suspended from it. When the mass is at rest,the spring is stretched through a distance of (Take acceleration due to gravity $g = \pi^2 = 10 \ m/s^2$): (in $m$)