Chapter5_4 - numbers to represent simple harmonic motion....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PHY3063 R. D. Field Department of Physics Chapter5_4.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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: numbers to represent simple harmonic motion. If we let t i Ae z = then t A z cos ) Re( = t A z sin ) Im( = z A = Re(z) |z| y x z = x +i y Im(z) SHM with amplitude A and angular frequency Phase Magnitude...
View Full Document

Ask a homework question - tutors are online