1. What is a Simple Pendulum?

A simple pendulum consists of a weight suspended from a pivot so that it can swing freely. When displaced, gravity causes it to oscillate with a regular period. The period is the time for one complete cycle (back and forth).

2. How Does the Calculator Work?

The calculator uses the pendulum period formula:

Where:

• \( T \) — Period (seconds)
• \( L \) — Length of pendulum (meters)
• \( g \) — Acceleration due to gravity (m/s²)
• \( \pi \) — Approximately 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 physics is crucial for clock design, seismometers, and various scientific instruments. It's also fundamental in studying harmonic motion.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why doesn't mass affect the period?
A: The restoring force and inertia both depend on mass, so they cancel out in the equations of motion.

Q2: What's the maximum angle for this formula to be accurate?
A: The small-angle approximation works well for angles less than about 15 degrees.

Q3: How does gravity affect the period?
A: Stronger gravity (larger g) decreases the period, making the pendulum swing faster.

Q4: What if my pendulum isn't "simple"?
A: For physical pendulums (real objects), the formula becomes more complex, involving moment of inertia.

Q5: Can I use this for a pendulum on another planet?
A: Yes! Just input the appropriate gravitational acceleration for that planet.