(main)[4]
A particle $P$ of mass $0.3\,\text{kg}$ is connected to one end of a light elastic string with natural length $0.6\,\text{m}$ and modulus of elasticity $45\,\text{N}$. The opposite end of the string is fixed at point $O$. The particle $P$ is released from rest at $O$ and drops vertically. Find the extension of the string when $P$ is at its lowest point.