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As a famous example for oscillations and kinematics in general, the pendulum is an often discussed topic. As part of this experiment, you will be using a prepared setup to generate your own measurement data and analyze it in Matlab.
Pendulum | Acceleration sensor | Arduino connection |
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- The experiment included typical questions regarding
- Frequency
- Mass
- Forces
- Amplitudes
- This experiment does not include us giving you all the equations, so you need to look up a few of them in your scripts or on the internet
- As an example: the relationship between mass, pendulum radius and frequency is given by
, but what that means is yours to find outMathinline body --uriencoded--T \approx 2\pi \sqrt%7B\frac%7BL%7D%7Bg%7D%7D
- As an example: the relationship between mass, pendulum radius and frequency is given by
- The experiment consists of 2 measurements
- Measurement A: simulate a slow, constant angular velocity while measuring accelerations in tangential and normal direction
- Measurement B: simulate a free oscillation by initially displacing the pendulum while measuring normal acceleration, tangential acceleration, angular velocity
- The measurements will be conducted by using our Matlab app at one of our computers
- The app is only for taking measurements, not for analyzing the data!
- There currently are only 2 pendulums, so please respect the time
- But please feel invited to observe different behaviors
- Afterwards, you will receive the measurement data via Email and post-process it to find the answers to our questions.
- We will also receive the same measurement data and calculate your solutions depending on your measurements
- DISCLAIMER:
- Treat the pendulums with respect and care! → No unnecessary swing-ups and/or games!
- Warn people around you, that they won't get hit by the pendulum's mass!
Matlab App:
| App after logging in with credentials | App after connecting to Arduino | App after performing Experiment A | App after performing Experiment B |
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Experiment 6A
This experiment is about understanding the dynamic behavior of the capacitive sensor and ignore the angle/angular velocity. The VIPS questions are related to the accelerations, their amplitudes, their mean and their relation to each other. The output accelerations should look similar to sine/cosine waves. Everything else is most likely a false measurement and has to be repeated.
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In part 6.2 you titled the sensor in different angles and read the values of the acceleration on the z-axis.
Find the acceleration values on the z-axis for six different angles and create a table.
Please enter your table values as follows:
| sensor angle in Degree ° | acceleration value on z-axis in m/(s^2) |
|---|---|
| 0° | 1 |
| 30° | 2 |
| 45° | 3 |
| 90° | 4 |
| 180° | 5 |
enter your table like this:
[0 1; 30 2; 45 3; 90 4; 180 5]
Please use the decimal point and give only numerical values in degree, respectively m/(s^2) as in this example: [0 1; 30 2; 45 3; 90 4; 180 5]
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In experiment 6C, you've conducted the measurement A, where you manually displaced the pendulum. You have noticed that the measured angle does not match the pendulum displacement you have observed during the measurement. You now want to recover the angle over time from the acceleration over time by using the relationship between deflection and gravity. Use the acceleration in the x axis to derive the maximum angle you have manually deflecteddisplaced.
What is the maximum angle, that you have displaced the pendulum to in degree?
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What is the centri fugal / centri petal accelerationexperienced acceleration experienced by the mass inside the accelerometer, where the acceleration in the x axis is equal to 9.81 m/(s^2)? Give the answer in m/(s^2)
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