A particle, P, of mass m, is moving in a horizontal circle, having centre O, with angular speed √g/4a. The particle is attached to one end of a light, elastic string of natural length 3a and modulus of elasticity 15/8 mg. The other end is attached to 8 a fixed point, C, which is vertically above O. The string makes an angle, θ, with 3 the downward vertical, where tan θ = 3/4. Find the elastic potential energy in the string and the kinetic energy of the particle P.