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you can use a variant that's happy to live inside $$ like multlined from mathtools,

---
title: "Untitled"
format: 
  pdf:
    keep-tex: true
    include-in-header: 
      - text: \usepackage{mathtools}
---

$$
\begin{multlined}
-m_2 a_2 - c_2 b_1 -c_2 b_2 - c_3 b_2 + c_3 b_3 \\
+ k_2 c_1 - k_2 c_2 - k_3 c_2 +k_3 c_3 = 0 
\end{multlined} 
$${#eq-eom3DOF}

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Answer selected by XinyanYang95
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math any issue related to math support in specific formats
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