$A$ body of mass $m$ is suspended to an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

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 $K$.

Three masses $100 \text{ g}$, $300 \text{ g}$, and $500 \text{ g}$ are suspended at the end of a spring and are in equilibrium. When the $500 \text{ g}$ mass is removed, the system oscillates with a period of $3 \text{ s}$. When the $300 \text{ g}$ mass is also removed, it will oscillate with a period of: (in $\text{ s}$)

When a mass $m$ is attached to a spring,it normally extends by $0.2\, m$. If the mass $m$ is given a slight additional extension and released,what will be its time period?

Three masses $700 \, g, 500 \, g$,and $400 \, g$ are suspended at the end of a spring as shown and are in equilibrium. When the $700 \, g$ mass is removed,the system oscillates with a period of $3 \, s$. When the $500 \, g$ mass is also removed,it will oscillate with a period of ...... $s$.

$A$ mass of $2 \, kg$ is attached to a spring with a spring constant of $50 \, N/m$. The block is pulled to a distance of $5 \, cm$ from its equilibrium position at $x = 0$ on a horizontal frictionless surface and released from rest at $t = 0$. Write the expression for its displacement at any time $t$.