7. A particle of mass 2 kg is attached to one end of a light elastic string of natural length 1 m and modulus of elasticity 50 N . The other end of the string is attached to a fixed point \(O\) on a rough horizontal plane and the coefficient of friction between the particle and the plane is \(\frac { 10 } { 49 }\). The particle is projected from \(O\) along the plane with an initial speed of \(5 \mathrm {~ms} ^ { - 1 }\).

1. Show that the greatest distance from \(O\) which the particle reaches is 1.84 m .
2. Find, correct to 2 significant figures, the speed at which the particle returns to \(O\).