Lwiva
JF-Expert Member
- Apr 17, 2015
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- 32,649
Cheke chea 👶👶Vin(t) is a symmetric square wave input with a frequency of 400 Hz and an amplitude of 4 V.
R = 470 Ω for the circuit, Calculate α, ωo, and ωd, use C = 0.1 uF, and L = 100 mH.
View attachment 3487742
Tunapewa RLC circuit ya mfululizo (series RLC)
👶a (alpha) – attenuation constant
👶w₀ (omega nought) – natural frequency
👶w_d (omega d) – damped natural frequency
👉
Tunapewa
R = 470 Ω
L = 100 mH = 0.1 H
C = 0.1 μF = 0.1
1)Alpha (α)
Formula
α = R / (2L)
Substuti
α = 470 / (2 × 0.1) = 2350 rad/s
2)Natural Frequency (w₀)
Formul
W₀ = 1 / √(LC)
Subustuti
w₀ = 1 / √(0.1 × 0.1×10⁻⁶)
= 1 / √(10⁻⁸) = 1 / (10⁻⁴) = 10⁴ rad/s = 10,000 rad/s
3)Damped Frequency (w_d)
Formula:
w_d = √(w₀² − α²)
Sabustuti
w_d = √((10,000)² − (2350)²)
= √(100,000,000 − 5,522,500)
= √94,477,500 ≈ 9719 rad/s
Majibu ya mwisho
👶α = 2350 rad/s
👶w₀ = 10,000 rad/s
👶w_d ≈ 9719 rad/s