From 2706d3db96483487a33b9bf573d073c2fd549bca Mon Sep 17 00:00:00 2001
From: Bowy La Riviere <b.m.lariviere@student.tudelft.nl>
Date: Thu, 25 Feb 2021 21:04:52 +0000
Subject: [PATCH] changes x to u for consistency
---
src/6_bonds_and_spectra_solutions.md | 8 ++++----
1 file changed, 4 insertions(+), 4 deletions(-)
diff --git a/src/6_bonds_and_spectra_solutions.md b/src/6_bonds_and_spectra_solutions.md
index ea7040ce..4388a91e 100644
--- a/src/6_bonds_and_spectra_solutions.md
+++ b/src/6_bonds_and_spectra_solutions.md
@@ -29,9 +29,9 @@ $$
1. In 1D, there are two normal modes and in 3D there are 4 normal modes
2. $$
\begin{cases}
- m \ddot{x}_1 & = -\kappa(x_1-x_2)\\
- M \ddot{x}_2 & = -\kappa(2x_2-x_1-x_3)\\
- m \ddot{x}_3 & = -\kappa(x_3-x_2)
+ m \ddot{u}_1 & = -\kappa(u_1-u_2)\\
+ M \ddot{u}_2 & = -\kappa(2u_2-u_1-u_3)\\
+ m \ddot{u}_3 & = -\kappa(u_3-u_2)
\end{cases}
$$
Where $m$ is the mass of the oxygen atoms and $M$ the mass of the carbon atom.
@@ -39,7 +39,7 @@ Where $m$ is the mass of the oxygen atoms and $M$ the mass of the carbon atom.
\omega = \sqrt{\frac{\kappa}{m}}
$$
4. $$
-\frac{x_1}{x_2} = -\frac{M}{2m}
+\frac{u_1}{u_2} = -\frac{M}{2m}
$$
5. $$
\omega = \sqrt{\frac{\kappa(2m+M)}{mM}}
--
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