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

In the figure given below. a block of mass $M =490\,g$ placed on a frictionless table is connected with two springs having same spring constant $\left( K =2 N m ^{-1}\right)$. If the block is horizontally displaced through ' $X$ 'm then the number of complete oscillations it will make in $14 \pi$ seconds will be $.........$

A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor, the velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$

Three mass and string system is in equilibrium. When $700\,gm$ mass is removed, then the system oscillates with a period of $3\,seconds$ . When the $500\,gm$ mass is also removed, then what will be new time period for system ..... $\sec$

A block of mass $m$ is suspended separately by two different springs have time period $t_1$ and $t_2$ . If same mass is connected to parallel combination of both springs, then its time period will be

If a spring has time period $T$, and is cut into $n$ equal parts, then the time period of each part will be