Question

Spring 2019 Problem Set 1: Mathematics of Waves Partial Review Assigned: 1/15/2019 Due: 1/22/2019 Problem 1 (15 pts) Reduce the function F(w)- a. to the rectangular form -a+ib and b, the polar form ΖΞ re

Answer 1

F(w) = A/negative w^2 - infinity w + w^2_0 = A/(negative w^2 + w^2_0) - infinity w = A/(negative w^2 + w^2_0 - I y w) negative w^2 + w^2_0 + infinity w (negative w^2 + w^2_0 + infinity w) = A (negative w^2 + w^2_0 + infinity w)/negative w^2 + w^2_0)^2 + y^2 w^2 F (w) = A(negative w^2 + w^2_0)/(negative w^2 + w^2_0)^2 + y^2 w^2 + I A y w/(negative w^2 + w^2_0) + y^2 w^2 (b) Hence r = squareroot a^2 + b^2 = A . (negative w^2 + w^2_0) + y^2 w^2 squareroot negative w^2 + w^2_0) + y^2 w^2