Simple Pendulum Calculator
Calculate period, frequency, and oscillation properties of simple pendulums
Calculate Pendulum Properties
Distance from pivot point to center of mass
Earth: 9.80665 m/s², Moon: 1.622 m/s²
Quick Gravity Presets:
Calculation Results
Formula used: T = 2π√(L/g)
• Period: T = 2π√(0.000/9.807) = 0.0000 s
• Frequency: f = 1/T = 0.0000 Hz
Pendulum Analysis
Example Calculation
Grandfather Clock Pendulum
Given: L = 2 m, g = 9.80665 m/s² (Earth)
Find: Period and frequency
Solution
T = 2π√(L/g) = 2π√(2/9.80665)
T = 2π√(0.2039) = 2π × 0.4516
T = 2.837 seconds
f = 1/T = 1/2.837 = 0.352 Hz
Pendulum Properties
Gravity on Different Bodies
Understanding Simple Pendulums
What is a Simple Pendulum?
A simple pendulum consists of a point mass (bob) suspended from a weightless string or rod of fixed length. It exhibits simple harmonic motion for small angular displacements, where the restoring force is provided by gravity.
Key Characteristics
- •Period is independent of mass and amplitude (small angles)
- •Restoring force is proportional to displacement
- •Energy conservation: KE ↔ PE conversion
- •Isochronous for small oscillations
Pendulum Equation
T = 2π√(L/g)
f = 1/T = (1/2π)√(g/L)
- T: Period (time for one complete oscillation)
- f: Frequency (oscillations per second)
- L: Length of pendulum (m)
- g: Acceleration due to gravity (m/s²)
Note: This formula is accurate for small angles (≤15°). For larger angles, more complex equations are needed.
Applications: Used in clocks, measuring gravity, seismometers, and physics demonstrations.