So, using the phasor approach, what is the solution to this circuit problem?

[hazim]

[SOLVED] phasor approach question

using phasor approach, determine the current i(t) in a circuit described by the integrodifferential equation: 4i + 8integral(idt) - 3di/dt = 50cos(2t + 75*)
the right side is so easy to convert to phasor form, but how can i convert the left side or how to solve such a problem?

 

[premagg]

dear it is simple.
just write I=dq/dt.you will get a second order differential equation.
you can solve it easily.

 

[premagg]

also integral(Idt)=q.

 

[Astronuc]

I think the point is to use the phasor format, and realize the for the phasor Ae^{i\omega{t}}, that

d/dt(e^{i\omega{t}})\,=\,i\omega{e^{i\omega{t}}}, and

\int(e^{i\omega{t}})dt\,=\,\frac{1}{i\omega}{e^{i\omega{t}}}\,=\,\frac{-i}{\omega}{e^{i\omega{t}}}