Comments on Critically damped oscillation issue
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Critically damped oscillation issue
I have a question about this circuit:(critically damped oscillation)
For a critically damped oscillation for a series RLC circuit the equation of current has this form I(t)=D1te^(-at)+D2e^(-at) where D2 =I(0+) and D1-aD2 = dI(0+)/dt=VL/L.
Due to L1 :I(0)=I(0+)=0A and by applying KVL in VL1=-VC1=-2V
And by substituting the values we get D1=-2A/s and D2 = 0A and we end up with an equation of I(t)=-2te^(-0.5t) but this cant be correct.What am I doing wrong?
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Your derivation is correct, you just missed the sign: $V_L=-V_C=2;\mathrm{V}$, because the capacitor charges with +2 V, and the discharge accounts for the negative sign on the inductor. The notation of $V_L=-V_C$ may be confusing, so think of it as $V_C=-V_L$, maybe it makes more sense.
Verifying your results is never a bad idea, so here it is:
I(R2) is plotted in blue while in black it's the test voltage, modelled as a function with the same format as your result, except for taking care of the delays (the uramp() part, such that it's zero until the event).
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