$A$ 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 .... $s$.

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?

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 $\text{ s}$)

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

$A$ mass $m$ attached to a spring oscillates every $2 \, s$. If the mass is increased by $2 \, kg$,then the time period increases by $1 \, s$. The initial mass is ..... $kg$.

Two springs of force constants $300 \, N/m$ (Spring $A$) and $400 \, N/m$ (Spring $B$) are joined together in series. The combination is compressed by $8.75 \, cm$. The ratio of energy stored in $A$ and $B$ is $E_A / E_B$. Then $E_A / E_B$ is equal to: