1. Two points \(A\) and \(B\) are 6 m apart on a smooth horizontal surface.

A light elastic string of natural length 2 m and modulus of elasticity 20 N , has one end attached to the point \(A\). A second light elastic string of natural length 2 m and modulus of elasticity 50 N , has one end attached to the point \(B\). A particle \(P\) of mass 3.5 kg is attached to the free end of each string.
The particle \(P\) is held at the point on \(A B\) which is 2 m from \(B\) and then released from rest.
In the subsequent motion both strings remain taut.

1. Show that \(P\) moves with simple harmonic motion about its equilibrium position.
2. Find the maximum speed of \(P\).
3. Find the length of time within each oscillation for which \(P\) is closer to \(A\) than to \(B\).