A particle of mass 0.1 kg lies on a smooth horizontal table on the line between two points \(A\) and \(B\) on the table, which are 6 m apart. The particle is joined to \(A\) by a light elastic string of natural length 2 m and modulus of elasticity 60 N , and to \(B\) by a light elastic string of natural length 1 m and modulus of elasticity 20 N . The mid-point of \(A B\) is \(M\), and \(O\) is the point between \(M\) and \(B\) at which the particle can rest in equilibrium. Show that \(M O = 0.2 \mathrm {~m}\). The particle is held at \(M\) and then released. Show that the equation of motion is $$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} t ^ { 2 } } = - 500 y$$ where \(y\) metres is the displacement from \(O\) in the direction \(O B\) at time \(t\) seconds, and state the period of the motion. For the instant when the particle is 0.3 m from \(M\) for the first time, find

1. the speed of the particle,
2. the time taken, after release, to reach this position.