PROBLEM SET 10

PROBLEM SET 10 - Note: you must show this explicitly;...

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PHYSICS 200 PROBLEM SET #10 Due November 18, 2009 Read Serway and Jewett Chapters 16 & 17. 1) For each of the following complex numbers, draw the location of the number on the complex plane. Also find for each of these numbers the real part, imaginary part, magnitude, phase, and complex conjugate. a) 1/(4 + 5 i ) b) (4 + 5 i ) 2 c) (4 + 5 i )/(4 – 5 i ) d) 7(4 + 5 i ) e) e (4 + 5 i ) 2) Consider the differential equation: x x =− ±± Where each dot represents a derivative with respect to time. You are told that two different functions a ( t ) and b ( t ) are solutions to this equation, but otherwise given no information about the specific form of a ( t ) and b ( t ). Show that a ( t ) + b ( t ) must also be a solution of the differential equation.
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Unformatted text preview: Note: you must show this explicitly; simply stating that the differential equation is linear is not sufficient. 3) Consider the differential equation: 2 x x = Where each dot represents a derivative with respect to time. You are told that two different functions a ( t ) and b ( t ) are solutions to this equation, but otherwise given no information about the specific form of a ( t ) and b ( t ). Show that a ( t ) + b ( t ) is not generally a solution of the differential equation. Note: you must show this explicitly; simply stating that the differential equation is nonlinear is not sufficient. Serway and Jewett: 16.22, 16.26, 17.23, 17.25, 17.35, 17.38...
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