# Homework Help: Steady State output for Wave Input

1. Dec 11, 2017

### soccer4life

1. Problem Statement
Find the steady state output yss(t) for the input u(t)=t-π in terms of an infinite sum of sinusoids.
We are given the transfer function as:

2. Relevant Equations

G(i) = ...
|G(ik)| = ...
Φ(ik) = ... (this is the angle)
yss(t) = βk||G(ik)|ei(kt+Φ(ik)) ***check that this is the correct formula please***

3. Attempt at Solution
I've found the following:
G(i)=1
|G(ik)| = (Any tips/tricks on how to input fractions/square roots into PF would be greatly appreciated...)
Φ(ik) =

Previously, the Fourier Series expansion was found, and is: the sum from 1 to infinity of Σ-2sin(kt)/k

I know that these values are right. However, I don't fully understand how to incorporate them into the steady state formula (assuming that my formula is correct)

Last edited by a moderator: Dec 15, 2017
2. Dec 16, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Dec 17, 2017

### vela

Staff Emeritus
Use the fact that $\sin\theta = \frac{e^{i\theta}-e^{-i\theta}}{2i}$.