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\includegraphics[max width=\textwidth, alt={}, center]{6b220343-1d64-4dbc-a42d-77967eef9c6d-06_264_839_260_653} A light elastic string has natural length 2 m and modulus of elasticity 39 N . The ends of the string are attached to fixed points \(A\) and \(B\) which are at the same horizontal level and 2.4 m apart. A particle \(P\) of mass \(m \mathrm {~kg}\) is attached to the mid-point of the string and hangs in equilibrium at a point 0.5 m below \(A B\) (see diagram).

1. Show that \(m = 0.9\).
   \(P\) is projected vertically downwards from the equilibrium position, and comes to instantaneous rest at a point 1.6 m below \(A B\).
2. Calculate the speed of projection of \(P\).