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

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).

$A$ block is fastened to a horizontal spring. The block is pulled to a distance $x = 10 \, cm$ from its equilibrium position (at $x = 0$) on a frictionless surface from rest. The total energy of the block at $x = 5 \, cm$ is $0.25 \, J$. The spring constant of the spring is $......... \, N \, m^{-1}$.

$A$ body of mass $m$ is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand,so that the spring is neither stretched nor compressed. Suddenly,the support of the hand is removed. The lowest position attained by the mass during oscillation is $4 \, cm$ below the point where it was held in hand.
$(a)$ What is the amplitude of oscillation?
$(b)$ Find the frequency of oscillation.

The angular frequency of a spring-block system is $\omega_0$. This system is suspended from the ceiling of an elevator moving downwards with a constant speed $v_0$. The block is at rest relative to the elevator. The lift is suddenly stopped. Assuming the downward direction as positive,choose the wrong statement:

$A$ block of mass $2 \ kg$ is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is $2 \ m$ and the spring constant is $200 \ N/m$. The block is pushed such that the length of the spring becomes $1 \ m$ and then released. At a distance $x \ m \ (x < 2)$ from the wall,the speed of the block will be: