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

Find the maximum amplitude for safe $SHM$ (the block does not topple during $SHM$) of a cubical block of side $a$ on a smooth horizontal floor as shown in the figure (the spring is massless). The spring is attached at a height of $2a/3$ from the floor.

$A$ body of mass $100 \ g$ is tied to a spring of spring constant $8 \ N/m$,while the other end of the spring is fixed. If the body moves in a circular path on a smooth horizontal surface with a constant angular speed of $8 \ rad/s$,then the ratio of the extension in the spring to its natural length will be: (in $:1$)

The springs shown in the figure are identical,each having a spring constant $K$. When mass $A = 4\, kg$ is attached,the elongation of the spring is $1\, cm$. If mass $B = 6\, kg$ is attached to the system of two springs in series as shown,the total elongation produced is ..... $cm$.

Two massless springs with spring constants $2k$ and $9k$ carry $50\,g$ and $100\,g$ masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then,the ratio of their respective amplitudes will be

Consider a spring-mass simple harmonic oscillator in one dimension. The mass of the particle is $m \text{ kg}$ and the spring constant is $k \text{ Nm}^{-1}$. At a given instant, the extension of the spring is $x \text{ m}$ and the speed of the particle is $v \text{ ms}^{-1}$. On the $x-v$ plane, if the graph of $v$ as a function of $x$ is a circle, then the correct option is: