6. A light elastic string, of natural length 0.8 m , has one end fastened to a fixed point \(O\). The other end of the string is attached to a particle \(P\) of mass 0.5 kg . When \(P\) hangs in equilibrium, the length of the string is 1.5 m .

1. Calculate the modulus of elasticity of the string.
   \(P\) is displaced to a point 0.5 m vertically below its equilibrium position and released from rest.
2. Show that the subsequent motion of \(P\) is simple harmonic, with period 1.68 s .
3. Calculate the maximum speed of \(P\) during its motion.
4. Show that the time taken for \(P\) to first reach a distance 0.25 m from the point of release is 0.28 s , to 2 significant figures.