$A$ spring is stretched by $0.2 \ m$ when a mass of $0.5 \ kg$ is suspended to it. The time period of the spring when the $0.5 \ kg$ mass is replaced with a mass of $0.25 \ kg$ is (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $s$)

Two springs,of force constants $k_1$ and $k_2$,are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$. If both $k_1$ and $k_2$ are made four times their original values,the frequency of oscillation becomes

When a mass $m$ is hung from the lower end of a spring of negligible mass,an extension $x$ is produced in the spring. The time period of oscillation is

Two springs of force constant $K$ and $2K$ are connected in series to a mass $M$ as shown in the figure. The frequency of oscillation of the mass is

Two bodies $M$ and $N$ of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal,the ratio of the amplitude of $M$ to that of $N$ is

$A$ simple harmonic oscillator consists of a particle of mass $m$ and an ideal spring with spring constant $k$. The particle oscillates with a time period $T$. The spring is cut into two equal parts. If one part oscillates with the same particle,the new time period will be