1. What is the Simple Pendulum Period?

The simple pendulum period is the time it takes for a pendulum to complete one full swing. It depends only on the length of the pendulum and the acceleration due to gravity, not on the mass of the pendulum bob or the amplitude of the swing (for small angles).

2. How Does the Calculator Work?

The calculator uses the simple pendulum formula:

Where:

• \( T \) — Period in seconds
• \( L \) — Length of the pendulum in meters
• \( g \) — Acceleration due to gravity (9.8 m/s² on Earth)

Explanation: The period increases with pendulum length and decreases with stronger gravitational acceleration.

3. Importance of Pendulum Period Calculation

Details: Understanding pendulum periods is crucial in physics, engineering (for clocks and seismometers), and even architecture (for building stability).

4. Using the Calculator

Tips: Enter pendulum length in meters and gravitational acceleration in m/s² (9.8 m/s² for Earth). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for any pendulum?
A: This formula is accurate for simple pendulums with small angles (less than 15°). For larger angles, more complex calculations are needed.

Q2: What if I'm not on Earth?
A: Simply change the gravity value to match your location (1.62 m/s² for Moon, 3.71 m/s² for Mars, etc.).

Q3: How does length affect the period?
A: Period is proportional to the square root of length. Doubling the length increases the period by √2 (about 1.414) times.

Q4: Why doesn't mass appear in the formula?
A: In simple pendulum motion, the restoring force and inertia both depend on mass, so it cancels out in the equations.

Q5: What's the longest pendulum period possible?
A: Theoretically unlimited as length increases, but practical limitations (like Earth's size) apply. The Foucault pendulum in the UN building has a 24-second period.