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https://texercises.com/exercise/damped-lc-oscillator-1/
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Exercise:
The amplitude of an LCR oscillator with frequency fO decreases exponentially with a half life of ThO. The resistance of the circuit is R. Calculate the inductance and the capacitance of this circuit.

Solution:
The half life of the amplitude for an LCR series circuit is T_/ tauln fracln delta fracln LR It follows for the inductance L LF fracThtimes Rln L approx resultLP Asing low damping T_/ gg T/f the frequency is f fracpisqrtLC It follows for the capacitance C CF fracpi^times f^times L C approx resultCP-
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Exercise:
The amplitude of an LCR oscillator with frequency fO decreases exponentially with a half life of ThO. The resistance of the circuit is R. Calculate the inductance and the capacitance of this circuit.

Solution:
The half life of the amplitude for an LCR series circuit is T_/ tauln fracln delta fracln LR It follows for the inductance L LF fracThtimes Rln L approx resultLP Asing low damping T_/ gg T/f the frequency is f fracpisqrtLC It follows for the capacitance C CF fracpi^times f^times L C approx resultCP-
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Attributes & Decorations
Branches
Damped Oscillations
Tags
damping, envelope, half-life, lc oscillator
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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