A particle \(P\) of mass 0.5 kg is attached to one end of a light elastic spring, of natural length 1.2 m and modulus of elasticity \(\lambda\) newtons. The other end of the spring is attached to a fixed point \(A\) on a ceiling. The particle is hanging freely in equilibrium at a distance 1.5 m vertically below \(A\).
Find the value of \(\lambda\).
The particle is now raised to the point \(B\), where \(B\) is vertically below \(A\) and \(A B = 0.8 \mathrm {~m}\). The spring remains straight. The particle is released from rest and first comes to instantaneous rest at the point \(C\).