P214soln2 - Prepared by Girma 1 Physics 214 Spring 2006...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Prepared by Girma 1 Physics 214 Spring 2006 Solution to Homework ] 2 Problem 1. ( a ). First we compute the real part and simplify x ( t ). Recall that a general complex number a + ib , where a and b are real, can be written as a + ib = a 2 + b 2 e i tan- 1 ( b/a ) . Thus x ( t ) = < [(5 + 7 i ) e iwt ] mm = < [ p 5 2 + 7 2 e i tan- 1 (7 / 5) e iwt ] mm = p 5 2 + 7 2 cos( wt + tan- 1 (7 / 5)) mm (1) v ( t ) = dx ( t ) dt =- p 5 2 + 7 2 w sin( wt + tan- 1 (7 / 5)) mm (2) x (10- 4 s ) = p 5 2 + 7 2 cos(10 4 rad/s 10- 4 s + tan- 1 (7 / 5)) mm =- 3 . 2 mm (3) v (10- 4 s ) =- p 5 2 + 7 2 10 4 s- 1 sin(10 4 rad/s 10- 4 s + tan- 1 (7 / 5)) mm =- 8 . 10 4 mm/s (4) ( b ). We read off from Equation (1) that A = 5 2 + 7 2 mm = 8 . 6 mm ( c ). See Figure (1).-4-2 2 4 6 Re LBracket1 x Smile RBracket1 LParen1 mm RParen1 7.25 7.5 7.75 8 8.25 8.5 8.75 9 Im LBracket1 x Smile RBracket1 LParen1 mm RParen1 t Equal 5 Plus 7i t Equal 10 Minus 4 s Minus 3.2 Plus 8.0 Imagi Figure 1: This plot shows the complex position x ( t ) = (5+7 i ) e iwt for = 10 4 rad/s and t 10- 4 s . The arrow on the right points to the position at t = 0 and the arrow on the left points to the position at t = 10- 4 s . Problem 2. Using the expression for the complex amplitude which was derived in the lecture and recalling again that a complex number a + ib can be written as a + ib = a 2 + b 2 e i tan- 1 ( b/a ) , where now a = f m ( 2 o- 2 ) / (( 2 o- 2 ) 2 + ) and b =- f m / (( 2 o-...
View Full Document

Page1 / 4

P214soln2 - Prepared by Girma 1 Physics 214 Spring 2006...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online