1. A particle \(P\) of mass 1.2 kg is attached to the midpoint of a light elastic string of natural length 0.5 m and modulus of elasticity \(\lambda\) newtons.

The fixed points \(A\) and \(B\) are 0.8 m apart on a horizontal ceiling. One end of the string is attached to \(A\) and the other end of the string is attached to \(B\). Initially \(P\) is held at rest at the midpoint \(M\) of the line \(A B\) and the tension in the string is 30 N .

1. Show that \(\lambda = 50\) The particle is now held at rest at the point \(C\), where \(C\) is 0.3 m vertically below \(M\). The particle is released from rest.
2. Find the magnitude of the initial acceleration of \(P\)
3. Find the speed of \(P\) at the instant immediately before it hits the ceiling.