Three masses $100 \text{ g}$, $300 \text{ g}$, and $500 \text{ g}$ are suspended at the end of a spring and are in equilibrium. When the $500 \text{ g}$ mass is removed, the system oscillates with a period of $3 \text{ s}$. When the $300 \text{ g}$ mass is also removed, it will oscillate with a period of: (in $\text{ s}$)

When a mass $M$ is attached to a spring of force constant $k$,the spring stretches by $l$. If the mass oscillates with amplitude $l$,what will be the maximum potential energy stored in the spring?

$A$ mass $m$ is attached to two springs of same force constant $K$,as shown in the following four arrangements. If $T_1, T_2, T_3$ and $T_4$ are the time periods of oscillation in the respective arrangements,in which case is the time period maximum?

$A$ body of mass $1 \,kg$ is suspended from a spring of negligible mass. Another body of mass $500 \,g$ moving vertically upwards hits the suspended body with a velocity of $3 \,ms^{-1}$ and gets embedded in it. If the frequency of oscillation of the system of the two bodies after collision is $\frac{10}{\pi} \,Hz$,the amplitude of the motion and the spring constant are respectively,

$A$ flat horizontal board moves up and down in $S.H.M.$ vertically with amplitude $A$. The shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is ..........

Three blocks of masses $700 \,g$,$500 \,g$,and $400 \,g$ are suspended at the end of a spring as shown in the figure and are in equilibrium. When the $700 \,g$ block is removed,the system has a period of oscillation of $3 \,s$. If both $700 \,g$ and $500 \,g$ blocks are removed,the period of oscillation becomes