Chapter1_5 - numbers to represent simple harmonic motion If...

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PHY4604 R. D. Field Department of Physics Chapter1_5.doc University of Florida Re(z) A z = Ae i ω t Im(z) φ = ω t t t Im(z) = Asin ω t Re(z) = Acost The Complex Plane φ i i e z z i z z e z z i z z = = = + = ) Im( ) Re( ) Im( ) Re( ) ( 2 1 cos ) Re( + = = = z z z z x ) ( 2 1 sin ) Im( = = = z z i z z y ) / arctan( x y = = + = zz y x z 2 2 sin cos i e i ± = ± 1 = ± i e 2 2 1 π i e i i ± = ± = Using Complex Numbers to Represent SHM We can use complex
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Unformatted text preview: numbers to represent simple harmonic motion. If we let t i Ae z ω = then t A z cos ) Re( = t A z sin ) Im( = z A = Re(z) |z| y x z = x +i y Im(z) φ SHM with amplitude A and “angular” frequency ω Phase Magnitude...
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