vault backup: 2025-06-30 16:28:41

Affected files:
.obsidian/workspace.json
Temporary/Gyroscope.md

.obsidian/workspace.json

@@ -344,9 +344,9 @@
           }
         ],
         "direction": "vertical",
-        "x": 2663,
+        "x": 1722,
-        "y": 1014,
+        "y": 1060,
-        "width": 527,
+        "width": 1052,
         "height": 795,
         "maximize": false,
         "zoom": 0.5

Temporary/Gyroscope.md

@@ -17,3 +17,8 @@ A drive frame (yellow) is oscillated (usually at 10-40kHz).
 When the sensor is rotated, the red mass is moved to either side and thus reducing/increasing the contacts to the blue sensing structure. See [How MEMS Accelerometer Gyroscope Magnetometer Work & Arduino Tutorial - YouTube](https://youtu.be/eqZgxR6eRjo?t=59) for more details.
 ![[Pasted image 20250630155216.png]]
 
+### Math
+- The base frequency of vibration: $\omega_r$
+- acceleration due to coriolis effect: $a_c = 2(\Omega \times v)$, where $v$ is a velocity and $\Omega$ is an angular rate of rotation.
+- The vibration has an expected in-plane velocity and position, which is not interesting. However, a rotation induces an out-of-plane motion $y_{op}$ which we can measure and thus determine the rate of rotation:
+$$ y_op = \frac{F_c}{k_{op}} = \frac{1}{k_{op}} 2m\Omega X_{ip}\omega_r cos(\omega_r t)$$