Update Content - 2023-01-10

content/zettels/mass_spring_damper_systems.md

@@ -1,6 +1,5 @@
 +++
 title = "Mass Spring Damper Systems"
-author = ["Dehaeze Thomas"]
 draft = false
 +++
 
@@ -13,7 +12,7 @@ Tags
 Let's consider Figure [1](#figure--fig:mass-spring-damper-system) where:
 
 -   \\(m\\) is the mass in [kg]
--   \\(ḱ\\) is the spring stiffness in [N/m]
+-   \\(k\\) is the spring stiffness in [N/m]
 -   \\(c\\) is the damping coefficient in [N/(m/s)]
 -   \\(F\\) is the actuator force in [N]
 -   \\(F\_d\\) is external force applied to the mass in [N]
@@ -42,14 +41,34 @@ with:
 -   \\(\xi\\) the damping ratio
 
 
-## Transmissibility {#transmissibility}
+## Transfer function {#transfer-function}
+
+
+### Voice Coil Actuator with flexible guiding {#voice-coil-actuator-with-flexible-guiding}
+
+```matlab
+%% Mechanical properties
+m = 1; % Mobile mass [kg]
+k = 1e6; % stiffness [N/m]
+xi = 0.01; % Modal Damping
+
+c = 2*xi*sqrt(k*m);
+```
+
+```matlab
+%% Transfer function from F [N] to x [m]
+G = 1/(m*s^2 + c*s + k);
+```
+
+
+### Transmissibility {#transmissibility}
 
 \begin{equation}
   \frac{x}{w}(s) = \frac{1}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}
 \end{equation}
 
 
-## Compliance {#compliance}
+### Compliance {#compliance}
 
 \begin{equation}
   \frac{x}{F\_d}(s) = \frac{1/k}{\frac{s^2}{\omega\_0^2} + 2 \xi \frac{s}{\omega\_0} + 1}