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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