$A$ mass $m$ is suspended from a spring of length $l$ and force constant $K$. The frequency of vibration of the mass is $f_1$. The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of the mass is $f_2$. Which of the following relations between the frequencies is correct?

One end of a long metallic wire of length $L$,area of cross-section $A$,and Young's modulus $Y$ is tied to the ceiling. The other end is tied to a massless spring of force constant $K$. $A$ mass $m$ hangs freely from the free end of the spring. It is slightly pulled down and released. Its time period is given by

Two springs of force constants $300 \, N/m$ (Spring $A$) and $400 \, N/m$ (Spring $B$) are joined together in series. The combination is compressed by $8.75 \, cm$. The ratio of energy stored in $A$ and $B$ is $\frac{E_A}{E_B}$. Then $\frac{E_A}{E_B}$ is equal to

$A$ small mass $m$,attached to one end of a spring with a negligible mass and an unstretched length $L$,executes vertical oscillations with angular frequency $\omega_{0}$. When the mass is rotated with an angular speed $\omega$ by holding the other end of the spring at a fixed point,the mass moves uniformly in a circular path in a horizontal plane. Then the increase in length of the spring during the rotation is

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

What will be the force constant of the spring system shown in the figure?