2 A particle \(P\) is moving in simple harmonic motion with centre \(O\). When \(P\) is 5 m from \(O\) its speed is \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and when it is 9 m from \(O\) its speed is \(\frac { 3 } { 5 } V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Show that the amplitude of the motion is \(\frac { 15 } { 2 } \sqrt { } 2 \mathrm {~m}\). Given that the greatest speed of \(P\) is \(3 \sqrt { } 2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), find \(V\).