Fill in the blank: $A$ spring is stretched by $3 \, cm$,its potential energy is $U_1$. If the spring is stretched by $6 \, cm$,its potential energy stored in it is $U_2 = ...... U_1$.

$A$ block of mass $m$ moving with speed $v$ compresses a spring through distance $x$ before its speed is halved. What is the value of the spring constant $k$?

An engine is attached to a wagon through a shock absorber of length $1.5 \, m$. The system with a total mass of $50,000 \, kg$ is moving with a speed of $36 \, km \, h^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest,the spring of the shock absorber gets compressed by $1.0 \, m$. If $90 \%$ of the energy of the wagon is lost due to friction,calculate the spring constant.

The work done in stretching a spring from $10 \ cm$ to $20 \ cm$ is:

$A$ body of mass $0.1 \ kg$ moving with a velocity of $10 \ m/s$ hits a spring (fixed at the other end) of force constant $1000 \ N/m$ and comes to rest after compressing the spring. The compression of the spring is .............. $m$.

When a long spring of $4 \ cm$ is stretched by $1 \ cm$,the potential energy stored in the spring is $U$. If it is stretched by $4 \ cm$,the potential energy stored in it is (in $U$)