/sci/ - Science & Math

anyone have any experience with ltspice?
trying to figure out why i keep getting a different answer on paper than on here

so v(n002,n001) is the voltage drop on the resistor at t=4.452202

if i use voltage division with complex numbers i get [math]\displaystyle \dfrac {10e^{-j \frac{\pi} {4}}}
{2+2j} * 2 [/math], where 2+2j is Zeq
that's equivalent to [math]5\sqrt{2}e^{-j \frac{\pi} {2}}[/math], so that would mean [math]v_r(t)=5\sqrt{2}\cos{(0.5t-\frac {\pi} {2} )}[/math], and v_r(4.452202)=5.60638 which is off from the value ltspice gave
in fact most times i've tried stuff with other numbers it's been close but definitely not a rounding error or accuracy problem (if it were, that voltage wouldn't be correct, and it is)

i doubt that it's my math that's wrong since this is how the professor teaches it and how the book does it
also as you can see the current plotted at the top is weird, it should be decaying from a value rather than going from negative to positive like that, when it should be I(t)=I0(1-e^t/T)

so uh what am i doing wrong here