Two identical particles each of mass $m$ are interconnected by a light spring of stiffness $k$. The time period for small oscillations is equal to:

The time period of simple harmonic motion of mass $M$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$,where the value of $\alpha$ is . . . . . . .

Five identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations $(i)$,$(ii)$ and $(iii)$ are in the ratio

Write the formula for the time period $(T)$ of a particle executing Simple Harmonic Motion $(SHM)$.

$A$ 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,

When a mass $m$ is connected individually with two springs $S_1$ and $S_2$,the oscillation frequencies are $n_1$ and $n_2$. If the mass $m$ is attached to the springs as shown in the figure,the oscillation frequency would be