FAQ on maple lab 5, Fall 2006 ========================================= L5.1 (A): How to select the value of k. To be under-damped means the solution x(t) has to have sine and cosine factors. That is, the characteristic equation must be a recipe case 3 equation with complex conjugate roots. A quadratic ar2+br+c=0 has complex conjugate roots <==> discriminant (term under the root sign of the quadratic formula) is negative. Formally, b2-4ac<0 characterizes discriminant negative. So, k satisfies an inequality, and you must choose k to make this inequality valid plus make a good graphic for x(t). L5.2 (B): Exact period of symbolic solution x(t). You are given something like x(t) =sin( 2 Pi t) + sin(6 Pi t). Then x(t) is a sum of terms of frequencies 2 Pi and 6 Pi, with corresponding periods 1 and 3. Then both terms have period 3 (3 is an integer multiple of 1). The actual x(t) is a combination of terms of frequencies w0 and 3(w0) with periods T1 and T2. They satisfy T2= 3(T1) and the reasoning goes like the example above. The answer is verified by clicking the mouse on the graphic at two successive maxima, then subtract the t-values displayed by maple for the two mouse clicks. L5.3 (A): The equation for C(w) is given in E&P page 355, equation (21). The maple code for it appears in the example below the problem statement. Make the example work, producing a plot with 3 curves. Then modify the code for the present conditions. L5.3 (B): To find maxima, click the mouse on the high spots in the graphic, and write the coordinates displayed by maple on a paper. Figure out which graph is which by a hand plot or by plotting just one curve. Curiously, some persons have trouble finding the displayed coordinates. Search for them in the maple window: maple likes to display them in a strange location in the upper left corner of the window.