Period, Frequency, and Angular Frequency Relationships
About This Diagram
This interactive infographic visualizes the mathematical relationships between the three key quantities describing oscillations: period (T), frequency (f), and angular frequency (ω).
The Three Quantities
Period (T)
- Definition: Time for one complete cycle
- Units: seconds (s)
- Example: A pendulum taking 2.0 s to swing back and forth has T = 2.0 s
Frequency (f)
- Definition: Number of cycles per second
- Units: hertz (Hz) = 1/s = s⁻¹
- Example: 0.5 Hz means half a cycle per second
Angular Frequency (ω)
- Definition: Radians per second of oscillation
- Units: rad/s
- Example: ω = π rad/s means the phase advances by π radians each second
Key Relationships
| Conversion | Formula |
|---|---|
| Period ↔ Frequency | f = 1/T, T = 1/f |
| Period → Angular Frequency | ω = 2π/T |
| Frequency → Angular Frequency | ω = 2πf |
Lesson Plan
Discussion Questions
- If you double the period, what happens to frequency?
- Why is there a factor of 2π in the angular frequency formula?
- A swing has period 3 seconds. What are f and ω?