From 2b4e580bac43098c2b51390998e2898b328f809a Mon Sep 17 00:00:00 2001 From: Worker Agent Date: Thu, 4 Jun 2026 16:25:40 -0500 Subject: [PATCH] fix(ch6): correct forced vibration coefficient collection --- chapters/ch06_mechanical_applications.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/chapters/ch06_mechanical_applications.tex b/chapters/ch06_mechanical_applications.tex index 1cfcbc7..acf7e69 100644 --- a/chapters/ch06_mechanical_applications.tex +++ b/chapters/ch06_mechanical_applications.tex @@ -441,16 +441,16 @@ Differentiating: Substitute into \cref{eq:forced_vibration}: \[ - \bigl[-m\omega^2 A - c\omega\omega B + kA\bigr]\cos(\omega t) - + \bigl[-m\omega^2 B + c\omega A + kB\bigr]\sin(\omega t) + \bigl[-m\omega^2 A + c\omega B + kA\bigr]\cos(\omega t) + + \bigl[-m\omega^2 B - c\omega A + kB\bigr]\sin(\omega t) = F_0\cos(\omega t). \] Equating coefficients: \[ \begin{cases} - (k - m\omega^2)A - c\omega B = F_0, \\ - c\omega A + (k - m\omega^2)B = 0. + (k - m\omega^2)A + c\omega B = F_0, \\ + -c\omega A + (k - m\omega^2)B = 0. \end{cases} \]