FAQ on maple lab 6, F2010
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L6.1 (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 have complex
conjugate roots. A quadratic ar2+br+c=0 has complex conjugate roots if
and only if the discriminant is negative. The DISCRIMINANT is the
expression under the root sign in the quadratic formula. Formally,
b^2-4ac<0 characterizes the discriminant negative. So, k satisfies an
inequality, and you must choose k to make this inequality valid, plus
also make an in nteresting graphic for x(t). There is some art involved.
L6.2 (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.
L6.3 (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.
L6.3 (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.