The spring constant provides the force required to change the length of a spring by an infinitesimal length if it has already been compressed by a length x. The force F = kx.

Given the force required as F = kx, we can find the work to be done to change the length of the spring from an initial length x1 to x2 as Int [F*dx], x= x1 to x=x2

W = Int [k*x dx], x = x1 to x=x2

=> kx^2/2, x = x1 to x=x2

Here the spring constant is given as 16N/m.

The work to be done is therefore 16*x^2/2, x = 0 to x = 5 cm

=> 16*(.05^2 – 0^2)/2

=> 16*0.0025/2

=> 0.02 J

**The required work to be done is 0.02 J**