A particle $P$ of mass $0.28{\text{ }}kg$ is attached to the mid-point of a light elastic string of natural length $4{\text{ }}m$.
The ends of the string are attached to fixed points $A$ and $B$ which are at the same horizontal level and $4.8{\text{ }}m$ apart. $P$ is released from rest at the mid-point of $AB$. In the subsequent motion, the acceleration of $P$ is zero when $P$ is at a distance $0.7{\text{ }}m$ below $AB$.
a) Show that the modulus of elasticity of the string is $20{\text{ }}N$.
b) Calculate the maximum speed of $P$.
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