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 $500 \,gm$ mass is also removed, it will oscillate with a period of ...... $s$

A force of $6.4\  N$ stretches a vertical spring by $0.1\ m$. The mass that must be suspended  from the spring so that it oscillates with a time period of $\pi/4\  second$ is .... $kg$

A body of mass $0.01 kg$ executes simple harmonic motion $(S.H.M.)$ about $x = 0$ under the influence of a force shown below : The period of the $S.H.M.$ is .... $s$

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 ..... $\sec$ ?

The force constants of two springs are ${K_1}$ and ${K_2}$. Both are stretched till their elastic energies are equal. If the stretching forces are ${F_1}$ and ${F_2}$, then ${F_1}:{F_2}$ is

A mass $m$ is suspended from the two coupled springs connected in series. The force constant for springs are ${K_1}$ and ${K_2}$. The time period of the suspended mass will be