hurricos/Lab1
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

format: number the derivations

Browse Source 
We borrowed the command from https://tex.stackexchange.com/a/42728.
This commit is contained in:
Martin Kennedy 2025-02-17 15:01:13 -05:00
parent 712e745538
commit c8a164d268
1 changed files with 4 additions and 2 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
Lab1.tex
View File

@ -14,6 +14,8 @@
\usepackage[a4paper, total={6in, 8in}]{geometry}
\usepackage{amsmath}
\newcommand\numberthis{\addtocounter{equation}{1}\tag{\theequation}}
\usepackage{cancel}
\usepackage{graphicx}
@ -103,7 +105,7 @@ expressed as:
&= V_{m}\sqrt{\frac{1}{T} \left[ \frac{t}{2} + \frac{1}{4\omega} \sin{(2\omega t)} \right]_{0}^T} \\
&= V_{m}\sqrt{\frac{1}{T} \left( \frac{T}{2} + \frac{1}{4\omega} \cancel{\sin{(2\omega T)}} - \frac{1}{4\omega} \cancel{\sin{(0)}} \right)} \\
&= V_{m}\sqrt{\frac{1}{\cancel{T}} \frac{\cancel{T}}{2}} \\
&= \frac{V_{m}}{\sqrt{2}}.
&= \frac{V_{m}}{\sqrt{2}}. \numberthis \label{deriv:ac}
\end{align*}
\subsection{Signal type ~\ref{type:acoffset}}
@ -127,7 +129,7 @@ expressed as:
&= V_{m}\sqrt{\frac{1}{T} \left( \frac{T}{2} + \frac{1}{4\omega} \cancel{\sin{(2\omega T)}} + \frac{2 V_{b}}{\omega V_{m}} \cancel{\sin{(\omega T)}} + T \left( \frac{V_{b}}{V_{m}} \right)^{2} - \frac{1}{4\omega} \cancel{\sin{(0)}} - \frac{2 V_{b}}{\omega V_{m}} \cancel{\sin{(0)}}\right)} \\
&= V_{m}\sqrt{\frac{1}{\cancel{T}} \left( \cancel{T} \right) \left( \frac{1}{2} + \left( \frac{V_{b}}{V_{m}} \right)^{2} \right)} \\
&= V_{m}\sqrt{\frac{1}{2} + \left( \frac{V_{b}}{V_{m}} \right)^{2}} \\
&= \sqrt{\frac{V_{m}^{2}}{2} + V_{b}^{2}}.
&= \sqrt{\frac{V_{m}^{2}}{2} + V_{b}^{2}}. \numberthis \label{deriv:acoffset}
\end{align*}
\section{Numerical Modeling Results}