Lab Report

Objective:

 To investigate the relationship between the length of a pendulum and its period using an AIoT-based system. You will use an Arduino system with an IR emitter and receiver alongside 3D-printed parts to adjust the length and mass of the pendulum.

Step 1: Setup of the Pendulum

1. Set up the Arduino with the IR emitter and receiver, as shown in the circuit diagram.

2. Assemble the pendulum using a 3D-printed mount, attach a bob (lead ball), and adjust the length of the string.

3. Measure the mass of the bob using a scale and record this value.

Mass of the pendulum bob (m): ________ kg

Step 2: Calibration

1. Upload the “AnalogRead” calibration code to the Arduino.

2. Determine the maximum and minimum readings of the IR sensor when the pendulum is at rest and swinging through the IR beam.

3. Update the “Pendulum” code with the recorded minimum and maximum sensor values.

AnalogRead Minimum: ________

AnalogRead Maximum: ________

Step 3: Measure the Period

1. Set the pendulum length L to your first value (e.g., 0.05 m).

2. Upload the updated “Pendulum” code to the Arduino with the corresponding length.

3. Displace the pendulum and let it swing freely. Allow it to oscillate 10 times, recording the time displayed on the OLED screen.

4. Calculate the average period by dividing the total time by 10.

Pendulum Length L: ________ m

 Average Period T: ________ s

Step 4: Repeat for Different Lengths

1. Repeat the measurement process for pendulum lengths of 0.07 m, 0.09 m, and 0.1 m.

2. Record the data in the table below.

Step 5: Analysis

1. Plot T² vs 4π²L. Calculate the slope of the graph, which should correspond to g, the gravitational constant.

2. Compare your experimental value of g to the theoretical value of 9.8 m/s² and calculate the percentage error.

1. Summarize the Experiment: Could you explain the main objective of the AIoT-enabled simple pendulum experiment and the methods used to collect data?

2. Data Analysis:

   • Using the data collected in your experiment, plot T² vs 4π²L.

   • Determine the slope of the line, which represents g. Include this plot in your report.c

3. Theoretical Validation:

   • Compare the experimental value of g obtained from the slope of your graph with the theoretical value of 9.8 m/s².

   • Calculate the percentage error.

4. Damping Investigation:

   • Based on the natural pendulum experiment, describe any observed damping effects (e.g., friction, air resistance).

   • How does the period change as the pendulum’s amplitude decreases?

5. Report Submission:

   • Submit a detailed report of your experiment, including the raw data, analysis, plots, and a brief discussion on the sources of error.

Problem 1: Length and Period Relationship

• A pendulum is set to oscillate with lengths of 0.05 m, 0.07 m, 0.09 m, and 0.1 m. The average periods T for these lengths are recorded as follows:

• Calculate T² vs 4π²L for each length.

• Plot T² vs 4π²L and find the slope. What is the experimental value of g based on this slope?

Problem 2: Damped Pendulum

In a damped pendulum system, the motion gradually decreases due to air resistance. Assume the damping coefficient b=0.05 kg/s, the mass of the bob is 0.1 kg, and the length of the string is 0.1 m. The initial angular displacement is 0.2 radians.

• Write the equation of motion for the damped pendulum.

• Simulate or plot the angular displacement θ(t) over time, considering the damping force.

Problem 3: Driven Pendulum

Consider a driven pendulum system where an external force is applied periodically to the pendulum. The mass of the pendulum bob is 0.1 kg, the length of the string is 0.1 m, and the driving force has an amplitude of 0.2 N with a driving frequency of 1.5 rad/s.

• Write the equation of motion for the driven pendulum.

• Discuss the resonance condition of the system. Under what driving frequency would the pendulum experience maximum amplitude oscillation?

Problem 4: Investigating Mass Dependence

 According to the theory, the period of a simple pendulum is independent of the mass of the pendulum bob. However, some deviations may occur in a real-world experiment due to friction or air resistance.

• Design an experiment using the AIoT setup to investigate the relationship between mass and period. How would you structure the experiment? What data would you collect to determine whether mass affects the period?

Problem 5: Error Analysis

In your AIoT simple pendulum experiment, you recorded the following data for length L=0.07 m and period T=0.52 s.

• If the time measurement has an uncertainty of 0.02 s, and the length measurement has an uncertainty of 0.001 m, calculate the percentage uncertainty in your value for the period squared T² and 4π²L.

• Discuss how these uncertainties affect the final value of g.

1. Worksheet (40%): Completeness and accuracy of theory, calculations, and explanations.

2. Assignment (30%): Detailed report, correct use of formulas, analysis, and discussion of results.

3. Problem Set (30%): Correctness of solutions, step-by-step calculations, and proper explanation.

Each lab group should download the Lab Report Template and fill in the relevant information as you experiment. Each group member should answer the Worksheet, Assignment, and Problem individually. Since each lab group will turn in an electronic copy of the lab report, rename the lab report template file. The naming convention is:

[Short Experiment Number]-[Student ID].PDF

Submit the Lab Report in PDf format