Summary of "Leyes del Péndulo con experimentos virtuales//ecuación del péndulo.//Laws of Simple Pendulum"

Main concepts and definitions

Simple pendulum: a small mass (bob) suspended from a light, inextensible string whose mass is negligible. The system is idealized (no friction or air resistance).
Pendulum length (l): measured from the pivot point to the center of gravity of the suspended mass (not just the string length).
Amplitude: angular displacement from the equilibrium (vertical) line (examples shown: 30° and 40°).
Physical pendulum: any rigid body oscillating about a pivot where the full mass distribution matters (examples: a metal part + sphere, or a bat). A physical pendulum differs from a simple pendulum because its moment of inertia and mass distribution affect its period.

Key formula and three fundamental laws

Period formula for small oscillations (simple pendulum): T = 2π √(l / g) where T = period, l = pendulum length (pivot to center of mass), and g = gravitational acceleration.
From that formula the three core laws:
1. Period ∝ √(length) — if l increases, T increases; if l decreases, T decreases.
2. Period ∝ 1/√(g) — if g increases, T decreases; if g decreases, T increases.
3. Period is independent of the mass of the bob — mass does not appear in the ideal formula for T.

Practical reminder: the formula assumes small amplitudes and ideal conditions (no friction, negligible string mass). For precise experiments, keep amplitudes small and account for non-ideal effects.

Experimental methodology (simulator)

General procedure used in the demonstrations:

Set pendulum parameters in the simulator: length l (pivot to center of mass), mass of bob, gravitational acceleration g, and amplitude (angle).
Displace the bob to the chosen amplitude and release.
Measure the period T as the time for one full cycle (extreme → equilibrium → opposite extreme → return to starting extreme). The video commonly times the return to the starting extreme as one cycle.
Repeat trials or run in slow motion to improve timing accuracy.
Record periods and compare across parameter changes.

Experimental results (representative)

1. Effect of length (mass and g held constant; no friction)

Observed periods for different lengths:

l = 0.30 m → T ≈ 1.10 s
l = 0.50 m → T ≈ 1.43 s
l = 0.70 m → T ≈ 1.69 s
l = 0.80 m → T ≈ 1.84 s
l = 1.00 m → T ≈ 2.04 s Conclusion: T increases approximately with √l, confirming law 1.

2. Effect of gravity (l = 0.80 m; mass constant)

Observed periods using different g values:

Earth (g ≈ 9.8 m/s²): T ≈ 1.90 s
Moon (much smaller g): T ≈ 4.19 s and 4.58 s in two trials (some variability)
Jupiter (much larger g): T ≈ 1.12 s Conclusion: Lower g → longer T; higher g → shorter T, confirming law 2.

3. Effect of mass (l and amplitude equal)

Example: two pendulums with l = 0.70 m and masses 0.50 kg and 1.50 kg (and other larger mass differences tried). Observed: both pendulums oscillate with the same period and remain synchronized. Conclusion: Mass does not affect T in the ideal simple pendulum, confirming law 3.

Additional points and practical remarks

The period can be used to infer local gravitational acceleration by rearranging T = 2π √(l / g).
The video emphasizes the idealization assumptions: negligible string mass, no air resistance or friction, and small amplitude for the small-angle approximation.
For physical (rigid-body) pendulums the simple formula does not apply; instead use the physical-pendulum expression involving the moment of inertia and the distance from the pivot to the center of mass.

Speakers / sources featured

Narrator / Host: Stress-Free Physics (also referred to in subtitles as “Physics Without Stress”).
Simulation used: University of Colorado pendulum simulator (PhET-style; referenced as PETS in subtitles).
Example environments: Earth, Moon, Jupiter (different g values used in the simulator).