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Understanding Periodic Functions
What are Periodic Functions?
A periodic function repeats its values at regular intervals. The most common form is f(x) = A·sin(ωx + φ) + C, where each component affects the function's behavior.
- A: Amplitude - determines height of oscillation
- ω: Angular frequency - affects period
- φ: Phase shift - horizontal displacement
- C: Vertical shift - moves function up/down
Important Relationships
Period Formula:
T = 2π/ω
where ω is angular frequency
Frequency Formula:
f = 1/T = ω/(2π)
where T is the period
Applications
Physics
- Wave motion
- Simple harmonic motion
- Electromagnetic waves
Engineering
- Signal processing
- Electrical circuits
- Vibration analysis