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by: Virgil Wyman

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# Engineer Math IV Differential Equations 22M 034

Marketplace > University of Iowa > Mathematics (M) > 22M 034 > Engineer Math IV Differential Equations
Virgil Wyman
UI
GPA 3.97

Staff

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COURSE
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KARMA
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## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Virgil Wyman on Friday October 23, 2015. The Class Notes belongs to 22M 034 at University of Iowa taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/227996/22m-034-university-of-iowa in Mathematics (M) at University of Iowa.

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Date Created: 10/23/15
22M2034 Engineering Math IV Differential Equations Computer Assignment 2 Amplitude modulation reso nance and damping 102003 due 1031 The solution of the initial value problem y My Ecoswt 110 MO 0 exhibits amplitude modulation AM the e ect being most pronounced when the constant it is chosen to be near to but not equal to the constant 1 The earmark of amplitude modulation is a high frequency oscillation taking place inside77 a low frequency one When the rest conditions y0 y 0 0 are replaced by other initial conditions the phenomenon at small times is a little less pronounced e the bottleneck77 the solution must pass through as the low frequency oscillation passes through equilibrium are more relaxed There will typically be large times to though for which the initial conditions at to are nearly rest conditions resulting in tight bottlenecks at times near to When it tends toward 1 we approach undamped resonance Problem 1 Do a graphical analysis of AM and undamped resonance along the general lines of the attached sample Maple session Here are the numbers you should use Suppose your your University number 00 A3A4 A5A6 A7A8 For the equation y My Ecoswt use A4 1 4i E 3 lt1 77I Let w range through various values near to the value of 1 to get the best graphical e ect For the case of non rest conditions take 110 7A67 40 A7 You won7t automatically get a good picture 7 you will probably need to tweak some of the tweakable parameters In the DEplot instruction the numbers in t 71010 y 722 stepsize 05 might all be productively changed to something else This is part of the art of graphically exploring and demonstrating physical phenomena Note that instead of solving the initial value problems in closed form and then graphing we just asked Maple directly for the graph This will be a useful technique later when we have nonlinear equations that don t have closed form solutions In these cases you can7t write an algebraic expression for the solution but you know its there The other Maple session attached demonstrates the transient nature of the e ect of initial conditions when damping is present Problem 2 Do your own dernonstration ofthis principle using the equation y by 02y E cosvt using your numbers 1 and E from 1 above and using A85 10 39

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