$A$ body of mass $m$ is suspended from 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

When a weight is applied to a spring,it stretches by an amount $x$. What is the energy stored in it? ($T$ is the tension force developed in the spring and $k$ is the spring constant.)

$A$ simple spring has length '$l$' and force constant '$K$'. It is cut into two springs of length '$l_1$' and '$l_2$' such that $l_1 = n l_2$ ($n$ is an integer). The force constant of the spring of length '$l_1$' is:

$A$ spring of force constant $k$ is cut into two equal halves. The force constant of each half is

$A$ block of mass $2 \,kg$ is connected to an ideal spring and is placed on a smooth horizontal surface. The spring is pulled to move the block and at an instant, the speed of end $A$ of the spring and speed of the block were measured to be $6 \,m/s$ and $3 \,m/s$, respectively. At this moment, the potential energy stored in the spring is increasing at a rate of $15 \,J/s$. Find the acceleration of the block at this instant. (in $\,m/s^2$)

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half length,the line $OA$ will