gen-define-resonance-frequency-and-give-one-short-worked-example-ff36

Define resonance frequency and give one short worked example.

# Resonance Frequency **Definition:** Resonance frequency is the natural frequency at which a system oscillates with maximum amplitude when disturbed or driven by an external periodic force. At this frequency, the system absorbs energy most efficiently because the driving frequency matches the system's natural oscillation frequency. ## Worked Example **Problem:** Find the resonance frequency of an LC circuit with inductance L = 10 mH and capacitance C = 100 μF. **Solution:** The resonance frequency for an LC circuit is: $$f_0 = \frac{1}{2\pi\sqrt{LC}}$$ Substituting values: - L = 10 mH = 10 × 10⁻³ H - C = 100 μF = 100 × 10⁻⁶ F $$f_0 = \frac{1}{2\pi\sqrt{(10 \times 10^{-3})(100 \times 10^{-6})}}$$ $$f_0 = \frac{1}{2\pi\sqrt{10^{-6}}}$$ $$f_0 = \frac{1}{2\pi \times 10^{-3}}$$ $$f_0 = \frac{1000}{2\pi} \approx 159 \text{ Hz}$$ **Answer:** The resonance frequency is approximately **159 Hz**.