Lab Report

Worksheet: AIoTs Vertical Torsion Pendulum with PLA Line and Magnetic Damping Experiment

Objective:

To understand the dynamics of a vertical torsion pendulum using a PLA line and investigate the effects of magnetic damping on the oscillatory motion.

Part 1: Experiment Setup

1. Materials Required:

   • 3D-printed rotating disk

   • PLA line (fixed on one end)

   • Optical encoder

   • Arduino and necessary wiring

   • Strong magnets

   • Ruler for measuring the radius

   • Scale for measuring the mass

   • Computer with LibreOffice Calc and Python installed

2. Procedure:

   • Measure the mass mmm of the rotating disk using a scale.

   • Measure the radius rrr of the rotating disk using a ruler.

   • Assemble the experimental setup with the 3D-printed parts, attaching the PLA line to the disk and fixing it at the other end.

   • Ensure the optical encoder is connected and functioning correctly.

   • Upload the provided code to the Arduino to begin capturing rotational data.

   • Perform the experiment by rotating the disk through a fixed angle and recording the oscillatory motion in the Arduino Serial Monitor.

Part 2: Data Collection and Analysis

1. Recording Data:

   • Open the Arduino Serial Monitor, rotate the disk by a fixed angle, and record the data.

   • Save the data in LibreOffice Calc as a CSV file.

2. Calculating the Moment of Inertia:

   • Use the formula

• to calculate the moment of inertia III of the disk. Ensure units are in kg·m².

Calculating the Torsion Constant:

• Perform a Fourier Transform using Python to determine the period T of the oscillations.

• Using the formula

1. • calculate the torsion constant K of the PLA line.

Part 3: Damping Experiment with Magnets

1. Adding Magnets:

   • Attach two strong magnets to the rotating disk and the optical encoder support.

   • Rotate the disk by a fixed angle and record the damped oscillations in the Arduino Serial Monitor.

   • Save the data in LibreOffice Calc.

2. Calculating the Damping Coefficient:

   • Analyze the data using Python to find the half-life of the damped oscillations.

   • Use the formula:

• to calculate the damping coefficient λ.

Repeat the Experiment Without Magnets:

• Perform the same procedure without magnets and compare the damping coefficients.

Question 1:

 You measured the mass of the rotating disk as 0.2 kg and the radius as 0.1 m. Calculate the moment of inertia I.

Question 2:

 Given a period T of 2 seconds and a moment of inertia I of 0.001 kg·m², calculate the torsion constant K of the PLA line.

Question 3:

 Using the experimental data, perform a Fourier Transform to determine the period of oscillation. Could you compare your result with the theoretical period calculation?

Question 4:

 If the half-life T1/2 is measured to be 3 seconds for the magnetic damping experiment, calculate the damping coefficient λ\lambdaλ.

Question 5:

 Compare the damping coefficients with and without magnets. Discuss the difference and explain why the damping coefficient changes.

Problem 1:

You are provided with a disk of mass 0.3 kg and radius 0.12 m. Perform the following:

• Calculate the moment of inertia I.

• Assume the torsion constant K is 0.05 N·m/rad, and calculate the theoretical period T of oscillation.

• If the experimental period differs, explain possible reasons for the discrepancy.

Problem 2:

 The damped oscillation data shows an amplitude reduction of 50% after 4 seconds with magnets attached. Use this information to calculate the damping coefficient λ.

Problem 3:

Design a similar experiment using a different material for the line (e.g., nylon or steel wire). How would the torsion constant and damping behavior differ compared to PLA? Could you provide a theoretical comparison? 

Problem 4:

For an underdamped oscillation system, derive the expression for the logarithmic decrement and explain how it relates to the damping coefficient.

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