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 . . . . . . .

Four massless springs whose force constants are $2K, 2K, K$ and $2K$ respectively are attached to a mass $M$ kept on a frictionless plane as shown in the figure. If mass $M$ is displaced in the horizontal direction,then the frequency of the oscillating system is:

The frequency of oscillation of the spring-mass system shown in the figure is:

If a vertical mass-spring system is taken to the moon,what will happen to its time period?

$A$ mass $m$ is suspended separately by two springs of spring constants $k_1$ and $k_2$. The time periods of oscillations in the two cases are $T_1$ and $T_2$ respectively. If the same mass $m$ is suspended by connecting the two springs in parallel (as shown in the figure),then the time period of the oscillation is $T$. The correct relation is:

Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratio of the time period of oscillation of the two $SHM$ is $\frac{T_b}{T_a} = \sqrt{x}$,where the value of $x$ is (Round off to the Nearest Integer).