Student Assignment:
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Shown is a solution of an equation of the type y"+py'+qy=cos(wt).
Answer:
(1) what are the numerical values of p, q, and w?
(2) what are the numerical values of y(0) and y'(0)?
(hint for y': use that y'=x and plot x(t))
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Change w to 0.0.
Plot the solution with this value of w ("submit all") and print.
(Note: the program gives you the option to print to file and save for
later printing or emailing). Use the Print button in the applet, NOT the
one for the browser.
(If you have difficulties printing, you can always try a "print screen"; most
computers allow you to do that.)
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Repeat with w=2.0, 3.0, 4.0, 5.0.
(Provide separate printouts for each of these values, please.)
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Write on a table the value of the amplitude "A" that you observe for the
oscillations (after transients). Just give rough estimates, using the scale
shown in the plot. (For instance, for w=1.0, the amplitude looks more or less
like 0.15; it may be useful to change the min and max of y to smaller values
to see better.) Do this for w=1,2,3,4,5.
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The amplitude formula given in page 421 of the textbook
is:
A = 1/(sqrt[(q-w^2)^2+p^2w^2]
Evaluate this formula for the values w=1,2,3,4,5, and compare with what the
plotting program gave you.
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Answer: at what value did you get the largest "A"? Prove
mathematically, using the formula, that this is what should have happened.
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Finally, repeat parts 2 and 3 after taking out the damping
term (-x).
View (General)
Instructions on using the JOde Applet
Using the applet written by: Marek Rychlik