2. A light elastic string has natural length 1.2 m and modulus of elasticity \(\lambda\) newtons. One end of the string is attached to a fixed point \(O\). A particle of mass 0.5 kg is attached to the other end of the string. The particle is moving with constant angular speed \(\omega \mathrm { rad } \mathrm { s } ^ { - 1 }\) in a horizontal circle with the string stretched. The circle has radius 0.9 m and its centre is vertically below \(O\). The string is inclined at \(60 ^ { \circ }\) to the horizontal. Find

1. the value of \(\lambda\),
2. the value of \(\omega\).