What is the work required to be done to compress a spring by 5 cm from the equilibrium position if the spring constant is 16N/m?

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