Pendulum Simulator Virtual Lab Procedure
Pendulum Lab Experiment 1: Length vs. Period
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Objective: Determine the mathematical relationship between the length of a pendulum and its time period (T).
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Controlled Variables: Mass = 1.0 kg, Gravity = 9.8 m/s² (Earth), Friction/Damping = OFF, Initial Amplitude = 10° (kept small to maintain the small-angle approximation).
Step-by-Step Procedure:
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Set the bob mass to 1.0 kg and gravity to 9.8 m/s² in the control panel, then turn the friction slider completely off.
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Adjust the string length slider to 0.20 m.
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Displace the pendulum bob to an initial angle of 10° on the canvas and release it.
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Use the integrated stopwatch tool to measure the time taken for 10 full oscillations (10 complete back-and-forth swings).
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Divide that total time by 10 to calculate the experimental period (T) of a single swing. Record this in your data table.
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Click Reset, increase the length to 0.40 m, and repeat the process. Complete the trials for lengths of 0.60 m, 0.80 m, and 1.00 m.
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Data Analysis Tip: Plot a graph of T^2 (Period squared) on the y-axis against Length (L) on the x-axis. A perfectly straight line verifies that the square of the period is directly proportional to its length.
Pendulum Lab Simulation Data Table
Use this pre-structured reference table to log your variables and verify your experimental findings against theoretical values.
String Length (L) | Mass (m) | Gravity (g) | Theoretical Period (T) | Simulated Period (T) | Time for 10 Swings (s) |
|---|---|---|---|---|---|
0.20 m | 1.0 kg | 9.8 m/s² | 0.90 s | Record from simulator | Record from simulator |
0.40 m | 1.0 kg | 9.8 m/s² | 1.27 s | Record from simulator | Record from simulator |
0.60 m | 1.0 kg | 9.8 m/s² | 1.55 s | Record from simulator | Record from simulator |
0.80 m | 1.0 kg | 9.8 m/s² | 1.79 s | Record from simulator | Record from simulator |
1.00 m | 1.0 kg | 9.8 m/s² | 2.01 s | Record from simulator | Record from simulator |
The Physics Behind the Pendulum Simulator
A simple pendulum consists of a concentrated mass (bob) suspended from a fixed pivot by a string of negligible mass. When deflected from its equilibrium axis, a restoring force accelerates the bob back toward the center.
The Dynamic Restoring Force
Unlike linear kinematics where forces act along flat planes, a pendulum moves along an arc. The weight of the bob (mg) splits into two distinct vector components:
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Radial component [mg * cos(theta)]: Acts parallel to the string to balance the tension force.
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Tangential restoring force [mg * sin(theta)]: Acts perpendicular to the string, pulling the bob back to the equilibrium position.
The Equation of Motion
Because the restoring force acts in direct opposition to the displacement angle (theta), the exact non-linear differential equation for an undamped pendulum is written as:
Angular Acceleration + (g / L) * sin(theta) = 0
The Small-Angle Approximation
When conducting manual calculations for your lab report, if the initial displacement remains small (less than 15°), the value of sin(theta) in radians is roughly equal to theta. This linearizes the system into standard simple harmonic motion (SHM), allowing us to calculate the definitive period (T) using the formula:
T = 2 * pi * square root(L / g)
The Physics Behind the Pendulum Simulator
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Q: Why does changing the mass of the bob have zero effect on the period?
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A: A heavier mass experiences a stronger gravitational pull downward, but its increased mass also means it possesses more inertia, requiring proportionally more force to accelerate. These two properties cancel each other out completely in the acceleration equations, making the swing cycle entirely independent of mass.
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Q: How does changing gravity modify the pendulum simulator's behavior?
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A: Gravity provides the restoring force. Higher gravity (like Jupiter at 24.8 m/s²) pulls the bob down much more aggressively, generating faster cycles and shorter periods. Lower gravity (like the Moon at 1.6 m/s²) results in weaker restoration forces, causing the pendulum to swing in slow motion with a long period.
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Q: Why do high release angles cause my experimental lab data to drift from the formula?
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A: The classic period formula [T = 2 * pi * square root(L / g)] relies strictly on the small-angle approximation where sin(theta) is roughly equal to theta. When you launch the pendulum from a steep angle (such as 60°), this mathematical assumption fails. It requires complex elliptic integrals to predict the true period, which will be noticeably longer than the simple theoretical value.
LEVEL UP YOUR PHYSICS GRADE
Pendulum Lab is just the warm-up. Unlock our High-Fidelity Simulations to master the core practicals of Physics. Dive into the Projectile Motion Simulator and the Free Fall Simulator to see the math come to life.