Let the initial position and speed of an over damped, non-driven oscillator be x0 and v0, respectively.
(a) Show that the values of the amplitudes A1 and A2 in Equation 3.44 have the values A1 = β2x0 + v0/ β2 – β1 and A2 = β1x0 + v0/ β2 – β1 where β1 β – w2 and β2 = β + w2.
(b) Show that when A1 = 0, the phase paths of Figure 3-11 must be along the dashed curve given by x = – β2x, otherwise the asymptotic paths are along the other dashed curve given by x = – β1x.