Simple Pendulum Calculator: Period, Length, Acceleration

What is a Simple Pendulum?

A simple pendulum is a theoretical model consisting of a point mass suspended by a massless, unstretchable string. It swings back and forth under the influence of gravity without friction. The simple pendulum is a fundamental concept in physics, used to study periodic motion and oscillations.

Formula

The period of a simple pendulum is given by the following equation:

\[ T = 2\pi \sqrt{\frac{L}{g}} \]

Where:

• \(T\) is the period of oscillation (time for one complete swing), measured in seconds (s)
• \(L\) is the length of the pendulum, measured in meters (m)
• \(g\) is the acceleration due to gravity, typically 9.8 m/s² on Earth's surface
• \(\pi\) is the mathematical constant pi, approximately 3.14159

Calculation Steps

Let's calculate the period of a simple pendulum with a length of 1 meter:

1. Identify the known values:
   • Length (L) = 1 m
   • Acceleration due to gravity (g) = 9.8 m/s²
2. Apply the period formula: \[ T = 2\pi \sqrt{\frac{L}{g}} \]
3. Substitute the known values: \[ T = 2\pi \sqrt{\frac{1 \text{ m}}{9.8 \text{ m/s²}}} \]
4. Perform the calculation: \[ T = 2\pi \sqrt{0.102} \approx 2.007 \text{ s} \]

Example and Visual Representation

Let's visualize a simple pendulum with our calculated period:

This visual representation shows:

• The pendulum at its equilibrium position (vertical)
• The path of the pendulum's swing (green arcs)
• The length of the pendulum (1 meter)
• The period of oscillation (approximately 2.007 seconds)