From 2306b0cfd24cff924392a497f3178baea6d642c3 Mon Sep 17 00:00:00 2001
From: Benjamin Chausse <benjamin@chausse.xyz>
Date: Tue, 3 Dec 2024 22:51:02 -0500
Subject: fix bug

---
 annexe/main.tex | 24 ++++++++++++------------
 1 file changed, 12 insertions(+), 12 deletions(-)

(limited to 'annexe/main.tex')

diff --git a/annexe/main.tex b/annexe/main.tex
index 072e927..b094801 100644
--- a/annexe/main.tex
+++ b/annexe/main.tex
@@ -163,21 +163,21 @@
 	\subsection{Décharge}
 	\begin{gather*}
 		\begin{align}
-			0         & = \vlt + V_C(t) + V_R(t)                                                           \\
+			0                             & = \vlt + V_C(t) + V_R(t)                                                           \\
 			\label{eq:rlc_decharge_initial}
-			0         & = \vlt+\frac{1}{C}\int I_(t)\dt + R_I(t)                                           \\
-			0         & = \ddt{2}\left[ \vlt + \frac{1}{LC}\iint\vlt\dt^2 + \frac{R}{L}\ddt{} \vlt \right] \\
-			0         & = \ddt{2}\vlt+ \frac{R}{L}\ddt{}\vlt +\frac{1}{LC}\vlt                             \\
-			0         & = \ddt{2}+\vlt+2\al\ddt{}\vlt+\ws                                                  \\
-			\nonumber\text{Posons que: }
+			0                             & = \vlt+\frac{1}{C}\int I_(t)\dt + R_I(t)                                           \\
+			0                             & = \ddt{2}\left[ \vlt + \frac{1}{LC}\iint\vlt\dt^2 + \frac{R}{L}\ddt{} \vlt \right] \\
+			0                             & = \ddt{2}\vlt+ \frac{R}{L}\ddt{}\vlt +\frac{1}{LC}\vlt                             \\
+			0                             & = \ddt{2}+\vlt+2\al\ddt{}\vlt+\ws                                                  \\
+			\nonumber \text{Posons que: } &
 			\vlt=Ae^{\la t} \Rightarrow
 			\ddt{}\vlt=\la Ae^{\la t} \Rightarrow
-			\ddt{2}\vlt=\la^{2}Ae^{\la t}                                                                  \\
-			0         & = \la^2Ae^{\la t} +2\al Ae^{\la t} + \ws Ae^{\la t}                                \\
-			0         & = Ae^{\la t} \left(\la^2 +2\al\la+\ws \right)                                      \\
-			0         & = \la^2 +2\al\la+\ws                                                               \\
-			\la_{1,2} & = \frac{-2\al\pm\sqrt{(-2\al)^2-4\ws}}{2(-2\al)}                                   \\
-			\la_{1,2} & = -\al\pm\sqrt{\al^2-\ws}
+			\ddt{2}\vlt=\la^{2}Ae^{\la t}                                                                                      \\
+			0                             & = \la^2Ae^{\la t} +2\al Ae^{\la t} + \ws Ae^{\la t}                                \\
+			0                             & = Ae^{\la t} \left(\la^2 +2\al\la+\ws \right)                                      \\
+			0                             & = \la^2 +2\al\la+\ws                                                               \\
+			\la_{1,2}                     & = \frac{-2\al\pm\sqrt{(-2\al)^2-4\ws}}{2(-2\al)}                                   \\
+			\la_{1,2}                     & = -\al\pm\sqrt{\al^2-\ws}
 		\end{align}
 	\end{gather*}
 	Puisque $R$ est de l'ordre des \si{\kohm} et $L$ de l'ordre des \SI{}{\mH}, on peut déterminer
-- 
cgit v1.2.3

