How Can Phasors Represent the Function g(t) in Complex Form?

Click For Summary

Homework Help Overview

The discussion revolves around the function g(t) = a cos(ωt) + b sin(ωt) and its representation in complex form using phasors. Participants are exploring how to express g(t) as the real part of the complex function keiΦeiωt, where k and Φ are constants representing amplitude and phase.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of Euler's formula to expand the complex expression and question how to equate terms to match g(t). There are inquiries about the meaning of the phase constant Φ and its role in the equations. Some participants express confusion over notation and the derivation of terms.

Discussion Status

There is ongoing exploration of the relationship between the coefficients of the trigonometric terms in g(t) and the expanded complex expression. Some participants have provided partial expansions and are questioning the correctness of their algebra, while others are guiding them to focus on matching coefficients to establish relationships between the constants.

Contextual Notes

Participants are navigating potential misunderstandings related to notation and the implications of variable relationships in the context of the problem. There is a noted confusion regarding the appearance of the phase constant Φ and its representation in the equations being discussed.

  • #31
sorry I am pretty lost here, do you mind working it out for me?
 
Physics news on Phys.org
  • #32
Dusty912 said:
sorry I am pretty lost here, do you mind working it out for me?
No, I will not do that, and no-one else on this forum should either.
Take the expression you had in post #23 and throw away the imaginary parts. Post what that leaves.
You should have the sum (or difference) of two terms, one with a cos(ωt) in it and the other with a sin(ωt). Call this expression R(t).
Similarly, g(t) has a cos(ωt) term and a sin(ωt) term. We need to arrange that R and g are the same function.
In order that R(t) and g(t) are to be identical functions, the cos term in one must be the same as the cos term in the other. Write that as an equation: (cos term extracted from g(t), complete with its coefficient there) = (cos term from R(t), complete with its coefficient there).
 

Similar threads

Complex periodic functions in a vector space
  • · Replies 28 ·
Replies
28
Views
4K
Given unit impulse response, obtain differential equation
  • · Replies 7 ·
Replies
7
Views
2K
Avoid unpleasant integrals in solving IVP
  • · Replies 3 ·
Replies
3
Views
2K
Linearly independent functions with identically zero Wronskian
  • · Replies 1 ·
Replies
1
Views
2K
Help with understanding BVP for the Heat equation (PDE)?
  • · Replies 2 ·
Replies
2
Views
2K
How should I use the averaging approximation to find this?
  • · Replies 3 ·
Replies
3
Views
2K
How should I find ## x_{2}(t) ## for this nonlinear integro-differential equation?
  • · Replies 6 ·
Replies
6
Views
3K
Green's Function: Solving a Differential Equation with a Green's Function
  • · Replies 8 ·
Replies
8
Views
2K
Green's functions: Logic behind this step
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Sinusoids as Phasors, Complex Exp, I&Q and Polar form
  • · Replies 4 ·
Replies
4
Views
2K