Let a spring of spring constant ‘k’ is stretched through a distance ‘x’ by the application of force fext.
Let x = o is the normal posting then the restoring force vector F brings the spring to its normal position.
By Hooke's law:
\(\overline F = k\bar x\) ........(1)
Also, \(\vec F_{ext} = -\vec F\)
so, equation (1) is \(\vec F_{ext} = -\vec F\)
\(\vec F_{ext} = +k x\) ........(2)
If the spring is stretched through a distance
\(dw = \vec F_{ext}. dx\)
\(dw = F_{ext} dx (Let\, \theta = 0^o)\)
\(dw = k\, x\, d\, x \)
On Integrating, we get total work done
