Chapter 8: Q20P (page 439)
Use L29 to verify L6, L13, L14, and L18
Short Answer
The values of L6, L13, L14 and L18 by use of is and,
Chapter 8: Q20P (page 439)
Use L29 to verify L6, L13, L14, and L18
The values of L6, L13, L14 and L18 by use of is and,
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Get started for freeIn Problems 13 to 15, find a solution (or solutions) of the differential equation not obtainable by specializing the constant in your solution of the original problem. Hint: See Example 3.
13. Problem 2
A solution containing 90% by volume of alcohol (in water) runs at 1 gal/min into a 100-gal tank of pure water where it is continually mixed. The mixture is withdrawn at the rate of 1 gal/min. When will it start coming out 50% alcohol?
Sketch on the same axes graphs of, and, and observe which way the graph shifts. Hint: You can, of course, have your calculator or computer plot these for you, but it's simpler and much more useful to do it in your head. Hint: What values of make the sines equal to zero? For an even simpler example, sketch on the same axes.
Use the methods of this section to solve the following differential equations. Compare computer solutions and reconcile differences.
Show that for a given forcing frequency , the displacement yand the velocity have their largest amplitude when .
For a given , we have shown in Section 6 that the maximum amplitude of y does not correspond to . Show, however, that the maximum amplitude of for a given does correspond to .
State the corresponding results for an electric circuit in terms of
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