When a mass $M$ is attached to a spring of force constant $k$,the spring stretches by $l$. If the mass oscillates with amplitude $l$,what will be the maximum potential energy stored in the spring?

$A$ small mass $m$ is suspended at the end of a wire having negligible mass,length $L$,and cross-sectional area $A$. The frequency of oscillation for the $S.H.M.$ along the vertical line is ($Y =$ Young's modulus of the wire).

Define the torsional constant for a spring.

As shown in the figure, a spring with spring constant $k = 150 \ N/m$ is kept in a stretched position by holding two masses of $1 \ kg$ and $200 \ g$ at a separation greater than the natural length of the spring. When the masses are released, assuming the horizontal surface to be frictionless, the angular frequency (in $SI$ units) of the system is:

The total spring constant of the system as shown in the figure will be

$A$ mass $m = 1.0\,kg$ is placed on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released,the mass executes simple harmonic motion. The spring constant is $k = 500\,N/m$. What is the amplitude $A$ of the motion,so that the mass $m$ tends to get detached from the pan? (Take $g = 10\,m/s^2$).