Probability — practice question

The ends of a light elastic string of natural length $0.8\,\text{m}$ and modulus of elasticity $\lambda\,\text{N}$ are fastened to fixed points $A$ and $B$, which are $1.2\,\text{m}$ apart at the same horizontal level. A particle of mass $0.3\,\text{kg}$ is attached to the middle of the string, and released from rest at the midpoint of $AB$. The particle falls vertically by $0.32\,\text{m}$ before it comes to instantaneous rest.