Module 03 • Virtual & Home Lab•Classical Mechanics & Oscillation
The Simple Pendulum
Investigate the relationship between string length, gravitational acceleration, and oscillation period. Discover why Galileo observed that a pendulum's swing time depends only on its length and gravity, not on its mass.
Safety Status: Safe at Home
Theoretical Formula:T = 2π√(L/g)
High School Level: Simple Harmonic Motion (T = 2π√(L/g))
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Live Physics Calculations
High SchoolTheoretical Formula: T = 2π√(L/g)
θ: +20.0°
Theoretical Period (T)
2.457s
Time required for one complete back-and-forth swing based on T = 2π√(L/g).
Small Angle Approximation (θ₀ ≤ 20°)
θ₀ = 20° • Small Angle (≤ 20°)In High School physics, we use sin(θ) ≈ θ (in radians). Under this small-angle approximation, the period T = 2π√(L/g) depends only on length L and gravity g, not on the release angle.
Frequency (f)
0.41 Hz
Angular Speed (ω)
2.56 rad/s
Peak Speed (v_max)
1.33 m/s
Simulation Controls
1.50 m
Presets:
9.81 m/s²
20°
Presets:
Digital Stopwatch
Measure swings manually to compare with theory
Count:
Elapsed Time
00:00.00
Measured Period (T_meas)
-- s
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Data Table
Record multiple trials with varying lengths, gravities, and release angles. Compare theoretical period against your measured stopwatch readings.
| Trial # | Length (L) | Gravity (g) | Angle (θ₀) | Theoretical (T) | Measured (T_meas) | Difference (ΔT) | Error % | Actions |
|---|---|---|---|---|---|---|---|---|
| #1 | 1.00 m | 9.81 m/s² | 20° | 2.006 s | s | ±0.004 s | 0.2% | |
| #2 | 2.00 m | 9.81 m/s² | 20° | 2.837 s | s | ±0.013 s | 0.5% |