5 A light elastic string of natural length \(a\) and modulus of elasticity \(\lambda \mathrm { mg }\) has one end attached to a fixed point \(O\) on a smooth horizontal surface. When a particle of mass \(m\) is attached to the free end of the string, it moves with speed \(v\) in a horizontal circle with centre \(O\) and radius \(x\). When, instead, a particle of mass \(2 m\) is attached to the free end of the string, this particle moves with speed \(\frac { 1 } { 2 } v\) in a horizontal circle with centre \(O\) and radius \(\frac { 3 } { 4 } x\).

1. Find \(x\) in terms of \(a\).
2. Given that \(\mathrm { V } = \sqrt { 12 \mathrm { ag } }\), find the value of \(\lambda\).