- #1
ongxom
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Homework Statement
vs = 300 (t>0)
vs = 150 (t<0)
v(0+)≠0
i(0+)≠0
R=50ohm
L=10H
C=1/100F
Determine v(t) when t>0
Homework Equations
The Attempt at a Solution
I wrote node voltage equation
(1/R)*v+(1/L)∫(v-vs)dt+C.(dv/dt)=0
First I do is get derivation to two sides of the equation to escape the integral, after that, replace all known datas, I got the equation
v''+2v+10v=10vs
So we have A(s)=s2+2s+10=0 ⇔ s=-1±3i
v(t)=vn+vp
which vn = 150V (cause we have t>0)
→ v(t)=150 + e[itex]^{-t}[/itex].(Acos3t+Bsin3t)
I am stucking on the way to find A and B constants, all I can do is below
v(0+)=150+A
v(0+)'=-A+3B