1. What is a Simple Pendulum?

A simple pendulum consists of a mass (bob) hanging from a fixed point that swings back and forth under gravity. The period is the time for one complete swing. This calculator computes the period based on length and gravity.

2. How Does the Calculator Work?

The calculator uses the simple pendulum formula:

Where:

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

Explanation: The period depends on the square root of the length divided by gravity. Longer pendulums swing more slowly, while stronger gravity makes them swing faster.

3. Importance of Pendulum Calculations

Details: Understanding pendulum motion is fundamental in physics and has applications in timekeeping (clocks), seismology, and engineering systems.

4. Using the Calculator

Tips: Enter length in meters and gravity in m/s² (Earth's gravity is 9.81 m/s²). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Does mass affect the period of a simple pendulum?
A: No, the period is independent of the mass of the bob for small oscillations.

Q2: What are the limitations of this formula?
A: It assumes small angle oscillations (<15°), no air resistance, and a massless string.

Q3: How does period change with length?
A: Period increases with the square root of length. Double the length increases period by √2 (~1.414) times.

Q4: What's the period on other planets?
A: Use different gravity values (Mars: 3.71 m/s², Moon: 1.62 m/s²) to calculate period changes.

Q5: What's the relationship between period and frequency?
A: Frequency (f) is the inverse of period (f = 1/T), measured in Hertz (Hz).