Option 1: Calculate Period from Frequency
Option 2: Simple Pendulum Period
How to Calculate Period: A Comprehensive Guide
In physics and wave mechanics, the period (T) is the time required for one complete cycle of a repeating event to occur. Whether you are studying sound waves, alternating current, or the rhythmic swing of a grandfather clock, understanding how to calculate the period is fundamental.
What is Period?
The period is the temporal duration of one cycle in a periodic event. It is the reciprocal of frequency. If a wave repeats many times per second, its period is very short. If it repeats slowly, its period is long. The standard SI unit for period is the second (s).
The Fundamental Formula
The simplest way to calculate the period is when you already know the frequency (f) of the oscillation.
- T: Period (seconds)
- f: Frequency (Hertz)
Calculating Period for a Simple Pendulum
For a physical object like a pendulum swinging at small angles, the period depends on the length of the string and the force of gravity. Interestingly, it does not depend on the mass of the weight.
- L: Length of the pendulum (meters)
- g: Acceleration due to gravity (approx. 9.81 m/s²)
If a pendulum has a length of 1 meter and the gravity is 9.81 m/s²:
T = 2 × 3.14159 × √(1 / 9.81)
T = 6.283 × √(0.1019)
T = 6.283 × 0.319
T ≈ 2.01 seconds
Period vs. Frequency
It is common to confuse period and frequency. While they are related, they measure different things:
- Period: "How long does one cycle take?" (Time per cycle)
- Frequency: "How many cycles happen in one second?" (Cycles per time)
Step-by-Step Instructions
Using Frequency
- Identify the frequency in Hertz (Hz).
- Divide 1 by the frequency.
- The result is the period in seconds.
Using Time and Number of Cycles
If you observe an event for a specific duration and count the cycles:
Frequently Asked Questions
Q: Does the amplitude affect the period of a pendulum?
A: For small angles (under 15 degrees), the amplitude has a negligible effect on the period. This is why pendulums were used in clocks for centuries.
Q: What is the period of a 60Hz power grid?
A: T = 1 / 60 = 0.01667 seconds, or 16.67 milliseconds.