A particle of mass \(2\,\text{kg}\) is attached to one end of a light elastic string of natural length \(0.8\) m and modulus of elasticity \(100\) N. The other end is attached to a fixed point \(O\) on a smooth horizontal surface.

The particle moves in a horizontal circle about \(O\), with the string taut and with constant angular speed \(5\,\text{rad s}^{-1}\). Find the extension of the string.