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:

If a watch with a wound spring is taken on to the moon,it

The force constant of a weightless spring is $16 \, N/m$. $A$ body of mass $1.0 \, kg$ suspended from it is pulled down through $5 \, cm$ and then released. The maximum kinetic energy of the system (spring + body) will be

The scale of a spring balance reading from $0$ to $10 \, kg$ is $0.25 \, m$ long. $A$ body suspended from the balance oscillates vertically with a period of $\pi / 10 \, s$. The mass suspended is ..... $kg$ (neglect the mass of the spring).

The springs in the figure are identical,but the length of the spring in $A$ is three times that in $B$. The ratio of the time periods $T_A/T_B$ is:

$A$ block of mass $2\,kg$ is attached to two identical springs,each with a spring constant of $20\,N/m$. The block is placed on a frictionless surface,and the outer ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position,it executes simple harmonic motion. The time period of oscillation is $\frac{\pi}{\sqrt{x}}$ in $SI$ units. The value of $x$ is $..........$