The variation of potential energy $U$ of a harmonic oscillator with respect to displacement $y$ is as shown in the figure. Find the spring constant $K$.

In the figure given below,a block of mass $M = 490 \, g$ placed on a frictionless table is connected with two springs having the same spring constant $(K = 2 \, N \, m^{-1})$. If the block is horizontally displaced through '$X$' m,then the number of complete oscillations it will make in $14 \pi$ seconds will be $.........$

The restoring force of a spring with a block attached to the free end of the spring is represented by

$A$ clock is designed based on the oscillations of a spring-block system suspended vertically in the absence of air resistance. Assume it shows the correct time when a spring of stiffness $k$ and a block of mass $m$ are used. If the block is replaced by another block of mass $4m$,choose the correct option.

$A$ mass $m = 8\,kg$ is attached to a spring as shown in the figure and held in position so that the spring remains unstretched. The spring constant is $k = 200\,N/m$. The mass $m$ is then released and begins to undergo small oscillations. The maximum velocity of the mass will be ..... $m/s$ $(g = 10\,m/s^2)$.

$A$ spring stretches by $2 \text{ mm}$ when it is loaded with a mass of $200 \text{ g}$. From the equilibrium position,the mass is further pulled down by $2 \text{ mm}$ and released. The frequency associated with the system and the maximum energy in the spring are . . . . . . $\text{Hz}$ and . . . . . . $\text{J}$,respectively. (Take $g = 10 \text{ m/s}^2$)