Doering_6_2S - 6.2 Natural Response of the Series RLC...

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6.2 – Natural Response of the Series RLC Circuit, Section 6-3 Summary Comparison: Results: vC(0) [V] vC min [V] vC max [V] fd [Hz] alpha [Np/s] Analysis 1.80 6.34 -8.52 8752 5000 Simulation 1.800 6.394 -8.515 8724 5000 Measurement 1.95 4.8 -6.9300 8990 6950 Relative Differences: Simulation -- Analysis 0.0% 0.9% -0.1% -0.3% 0.0% Measurement -- Analysis 8.3% -25.1% -18.7% 2.7% 39.0% Analytical Solution:
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Initial value when t=0: 1.800 V Damped oscillation frequency: fd = ω 0 / 2 π = 8.725 kHz
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MathScript script and plot showing maximum and minimum values: Maximum value = 6.34 V Minimum value = -8.52 V
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myDAQ Results: Function Generator setup:
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Oscilloscope measurements: vC(0) = 1.95 V
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Maximum value = 4.75 V Minimum value = -6.93 V
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Oscillation frequency: Time for four oscillation periods = 445us 445/4 = 111.3us period 8.99 kHz NOTE: The 5us resolution is the upper limit of the myDAQ. Damping coefficient: ln(6.93/0.326) / 440us = 6950 Np/s Further Exploration: The measured inductor resistance (DMM ohmmeter) is 89.1 ohms; this is 27% of the 330-ohm resistor, a
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Doering_6_2S - 6.2 Natural Response of the Series RLC...

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