5 One end of a light elastic string of natural length 0.3 m and modulus of elasticity 6 N is attached to a fixed point \(O\) on a smooth horizontal plane. The other end of the string is attached to a particle \(P\) of mass 0.2 kg , which moves on the plane in a circular path with centre \(O\). The angular speed of \(P\) is \(\omega \mathrm { rad } \mathrm { s } ^ { - 1 }\).

1. For the case \(\omega = 5\), calculate the extension of the string.
2. Express the extension of the string in terms of \(\omega\), and hence find the set of possible value of \(\omega\).