1. What is the Simple Pendulum Equation?

The simple pendulum equation calculates the period of oscillation for an idealized pendulum consisting of a point mass suspended from a fixed point with a massless string or rod, swinging under gravity with small angular displacements.

2. How Does the Calculator Work?

The calculator uses the pendulum period equation:

Where:

• \( T \) — Period of oscillation (seconds)
• \( L \) — Length of pendulum (meters)
• \( g \) — Acceleration due to gravity (m/s²)
• \( \pi \) — Mathematical constant (~3.14159)

Explanation: The period depends only on the length of the pendulum and the strength of gravity, not on the mass of the bob or the amplitude of swing (for small angles).

3. Importance of Pendulum Calculations

Details: Understanding pendulum dynamics is fundamental in physics and engineering, with applications in timekeeping, seismology, and mechanical systems.

4. Using the Calculator

Tips: Enter length in meters and gravitational acceleration in m/s² (9.81 m/s² on Earth's surface). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What assumptions does this equation make?
A: It assumes small angle oscillations (<15°), no air resistance, a point mass, and a massless string/rod.

Q2: How does gravity affect the period?
A: Greater gravity decreases the period (pendulum swings faster). On the Moon (g≈1.62 m/s²), the same pendulum would have a longer period.

Q3: What if my pendulum has a large amplitude?
A: For larger angles, the period increases slightly. The exact solution requires elliptic integrals.

Q4: Can this be used for real pendulums?
A: For physical pendulums with distributed mass, a different equation accounting for moment of inertia is needed.

Q5: Why is the mass not in the equation?
A: In simple harmonic motion under gravity, the mass terms cancel out - all objects accelerate at the same rate regardless of mass.