
ODE and locus
Hi,
I need some checking for what I did:
Solve the ODE $\displaystyle
\frac{dx[t]}{dt}=\frac{y[t]}{RC}+ \frac{dy[t]}{dt}
$ given x(t)=e^(iωt)
I assume y(t)=A*e^(iωt)
I found:
A=(i*ω*RC)/(RC+1)
y(t)=(i*ω*RC)(e^(iωt))/(RC+1)
then I am asked to express y(t) as a phasor:
I got: y(t)=(ω*RC)(e^(iωt+(π/2))/(RC+1)
since i=e^(π/2)
Am I right?
finally and here I have not found the answer:
Express the locus in the form of Zo+ρ*e^(i*θ )
calculate Z0, Rho and the range of theta.
If what I have dne is rightHow can I find the locus.
I know that there was recently a post about it but it was not helpful in my case.
thank you