5 A particle \(P\) of mass 0.05 kg is suspended from a fixed point \(O\) by a light elastic string of natural length 0.5 m and modulus of elasticity 2.45 N .
- Show that the equilibrium position of \(P\) is 0.6 m below \(O\).
\(P\) is held at rest at a point 0.675 m vertically below \(O\) and then released. At time \(t \mathrm {~s}\) after \(P\) is released, its downward displacement from the equilibrium position is \(x \mathrm {~m}\). - Show that \(\frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } = - 98 x\).
- Find the value of \(x\) and the magnitude and direction of the velocity of \(P\) when \(t = 0.2\).