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Voltage of tank circuit is invalid
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In a previous question we found that for a critically damped oscillation:
$$ I(t) = 2 t e^{-0.5 t} $$But if we integrate to find the voltage through the capacitor:
$$ V_{CO} + \frac{1}{C} \cdot \int_0^t{I(t)}dt $$the integral is always a positive value which doesn't make any sense since the capacitor is being discharged.
What am I doing wrong here? Help appreciated!
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