The variation with extension 
of the force 
acting on a spring is shown in the Fig. 1 below
Fig. 1
The spring of unstretched length 
has one end attached to a fixed point, as shown in the figure below.
A block of weight 
is then attached to the spring. The block is then released and begins to move downwards. At one instant, as the block is continuing to move downwards, the spring has a length of 
, as shown in Fig. 3. Assume that the air resistance and the mass of the spring are both negligible. For the change in length of the spring from to :
use Fig. 1 to show that the increase in elastic potential energy of the spring is 
calculate the decrease in gravitational potential energy of the block of weight .
.
