One end of a light elastic string of natural length $0.4{\text{ }}m$ and modulus of elasticity $20{\text{ }}N$ is attached to a fixed point $O$. The other end of the string is attached to a particle $P$ of mass $0.25{\text{ }}kg$. $P$ hangs in equilibrium below $O$.
a) Calculate the distance $OP$.
The particle $P$ is raised, and is released from rest at $O$.
b) Calculate the speed of $P$ when it passes through the equilibrium position.
c) Calculate the greatest value of the distance $OP$ in the subsequent motion.
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