An elastic spring under a tension of $3 \,N$ has a length $a$. Its length is $b$ under a tension of $2 \,N$. For its length $(3a - 2b)$, the value of tension will be . . . . . . $N$.

Initially,a spring is at its natural length. $A$ block of mass $2 \, kg$ is attached to the lower end,and a block of mass $0.25 \, kg$ is at the top. If the system is released from the position where the spring is at its natural length,find the maximum force exerted by the system on the floor? (in $N$,take $g = 10 \, m/s^2$)

The length of a spring is $\alpha$ when a force of $4\,N$ is applied on it and the length is $\beta$ when $5\,N$ force is applied. Then the length of the spring when $9\,N$ force is applied is

$A$ light spring of length $20 \ cm$ and force constant $2 \ kg/cm$ is placed vertically on a table. $A$ small block of mass $1 \ kg$ falls on it. The height $h$ from the surface of the table at which the block will have the maximum velocity is ............... $cm$.

$A$ block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has a force constant $k$. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

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.)