A particle executes $SHM$ with amplitude of $20 \,cm$ and time period is $12\, sec$.  What is the minimum time required for it to move between two points $10\, cm$ on  either side of the mean position ..... $\sec$ ?

In the following questions, match column $-I$ with column $-II$ and choose the correct options

A block of mass $m$ hangs from three springs having same spring constant $k$. If the mass is slightly displaced downwards, the time period of oscillation will be

In the reported figure, two bodies $A$ and $B$ of masses $200\, {g}$ and $800\, {g}$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be $.....\,{rad} / {s}$ when ${k}=20 \,{N} / {m} .$

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 masses $700g, 500g$ and $400g$ are suspended at the end of a spring a shown  and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a  period of $3\,seconds$, when the $500g$ mass is also removed, it will oscillate with a period of .... $s$