1 One end of a light elastic string of natural length 0.7 m is attached to a fixed point \(A\) on a smooth horizontal surface. The other end of the string is attached to a particle \(P\) of mass 0.3 kg which is held at a point \(B\) on the horizontal surface, where \(A B = 1.2 \mathrm {~m}\). It is given that \(P\) is released from rest at \(B\) and that when \(A P = 0.9 \mathrm {~m}\), the particle has speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Calculate the modulus of elasticity of the string.