1 The point \(O\) is on the fixed horizontal line \(l\). Points \(A\) and \(B\) on \(l\) are such that \(O A = 0.1 \mathrm {~m}\) and \(O B = 0.5 \mathrm {~m}\), with \(A\) between \(O\) and \(B\). A particle \(P\) oscillates on \(l\) in simple harmonic motion with centre \(O\). The kinetic energy of \(P\) when it is at \(A\) is twice its kinetic energy when it is at \(B\). Find the amplitude of the motion.