A spring block system starts executing SHM in a stationary lift when left under gravity. The wire of the lift breaks at a moment when the spring comes in its natural length. Then.

A particle of mass $m$ is attached to four springs with spring constant $k,k,2k$ and $2k$ as shown in the figure. Four springs are attached to the four corners of a square and a particle is placed at the center. If the particle is pushed slightly towards any side of the square and released, the period of oscillation will be

In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k,$ the frequency of oscillation of given body is:

In the given figure, a mass $M$ is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is $k.$ The mass oscillates on a frictionless surface with time period $T$ and amplitude $A.$ When the mass is in equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will be:

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 ratios of time period of oscillation of the two SHM is $\frac{T_b}{T_a}=\sqrt{x},$ where value of $x$ is ______.

(Round off to the Nearest Integer)

Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :

In the reported figure, two bodies $A \mathrm{and} B$ of masses $200 \mathrm{g}$ and $800 \mathrm{g}$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______  $\mathrm{rad} {\mathrm{s}}^{-1}$ when $k=20 \mathrm{N} {\mathrm{m}}^{-1^{}}$.

A tray of mass $12 \mathrm{kg}$ is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of $1.5 \mathrm{s}$. The spring constant of each spring is