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fix(ch6): correct forced vibration coefficient collection

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2026-06-04 16:25:40 -05:00
parent 2666b3ac67
commit 2b4e580bac
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8
chapters/ch06_mechanical_applications.tex
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@@ -441,16 +441,16 @@ Differentiating:
Substitute into \cref{eq:forced_vibration}: Substitute into \cref{eq:forced_vibration}:
\[ \[
\bigl[-m\omega^2 A - c\omega\omega B + kA\bigr]\cos(\omega t) \bigl[-m\omega^2 A + c\omega B + kA\bigr]\cos(\omega t)
+ \bigl[-m\omega^2 B + c\omega A + kB\bigr]\sin(\omega t) + \bigl[-m\omega^2 B - c\omega A + kB\bigr]\sin(\omega t)
= F_0\cos(\omega t). = F_0\cos(\omega t).
\] \]
Equating coefficients: Equating coefficients:
\[ \[
\begin{cases} \begin{cases}
(k - m\omega^2)A - c\omega B = F_0, \\ (k - m\omega^2)A + c\omega B = F_0, \\
c\omega A + (k - m\omega^2)B = 0. -c\omega A + (k - m\omega^2)B = 0.
\end{cases} \end{cases}
\] \]