My textbook says the an object undergoing undamped, under-driven harmonic motion (http://romano.physics.wisc.edu/lab/manual/img279.gif) does NOT have its maxima at the points where the displacement curve makes contact with the exponential envelope curve. How can this be the case?? Doesn't the graph clearly imply that the maxima are indeed the peaks of the decaying cosine curve (that do make contact with the exponential wrapper)?? The text goes on to say that the maxima actually correspond not to the x(t) vs. t plot -- but to the dx(t)/dt (the velocity) plot, specifically where dx(t)/dt = 0. I can partially understand this since at the maxima -- velocity does equal 0! It then states that the displacement ratios between successive maxima are constant. I can see the constancy of the maxima ratios, but not the basis on dx(t)/dt over the visual interpretation -- let alone the assertion that successive maxima ratios are constant. Comments? Thanks!