Update content - 2026-10-14

content/zettels/mass_spring_damper_systems.md

@@ -31,24 +31,24 @@ Let's consider [Figure 1](#figure--fig:mass-spring-damper-system) where:
 Transmissibility:
 
 \begin{equation}
-  \frac{x}{w}(s) = \frac{c s + k}{m s^2 + c s + k} = \frac{2 \xi \frac{s}{\omega\_0} + 1}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}
+  \frac{x}{w}(s) = \frac{c s + k}{m s^2 + c s + k} = \frac{2 \zeta \frac{s}{\omega\_0} + 1}{\frac{s^2}{\omega\_0^2} + 2 \zeta \frac{s}{\omega\_0} + 1}
 \end{equation}
 
 Compliance:
 
 \begin{equation}
-  \frac{x}{F}(s) = \frac{x}{F\_d}(s) = \frac{1}{m s^2 + c s + k} = \frac{1/k}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}
+  \frac{x}{F}(s) = \frac{x}{F\_d}(s) = \frac{1}{m s^2 + c s + k} = \frac{1/k}{\frac{s^2}{\omega\_0^2} + 2 \zeta \frac{s}{\omega\_0} + 1}
 \end{equation}
 
 with:
 
 -   \\(\omega\_0 = \sqrt{k/m}\\) the natural frequency in [rad/s]
--   \\(\xi = \frac{1}{2} \frac{c}{\sqrt{km}}\\) the damping ratio [unit-less]
+-   \\(\zeta = \frac{1}{2} \frac{c}{\sqrt{km}}\\) the damping ratio [unit-less]
 
 A quality factor \\(Q\\) can also be defined:
 
 \begin{equation}
-Q = \frac{1}{2\xi}
+Q = \frac{1}{2\zeta}
 \end{equation}
 
 This corresponds to the amplification at the natural frequency \\(\omega\_0\\).