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# when i am alowed to use phasors

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#### transgalactic

##### Banned
Vc''+Vc=3cos(2t)
Vc(0)=2
Vc'(0)=3

i was told that some thing should converge on t->inf

is it the ZIR ?

Hi,

Looks like the DC component.

What do you mean when do you use phasors? THey're just another way to write complex numbers.

Hi DK,

I was a little confused by this last question too.
We havent heard from transgalactic for a while now, i wonder if he/she
took off to some other galaxy by now

I think they allow phasors but have banned disruptors

i was told that when i have a sinus input in m diff equation
than there are case when i am not allowed to use
foorier transformation(phasors)

but i have to solve it like a normal diff equation with a sinus in the right side

what is that case?

Phasors can be used in any circuit with a phase shifted power source. They can not be used in underdamped step input circuits because the exponential component adds its own phase component to the ringing component, so:
What equation for Vc can you add to its 2nd derivitive to get 3cos(2t)?

Well, if Vc = Acos(βt) then Vc' = -Aβsin(βt) and Vc'' = -Aβ²cos(βt) so that:

-Aβ²cos(βt) + Acos(βt) = 3cos(2t)
A(-β² + 1)cos(βt) = 3cos(2t)
so: β = 2
and: A(-β² + 1) = 3
A = 3/(-2² + 1)
= -1
so: Vc = -cos(2t) V
I guess the right hand waveform is shifted 180deg from the solution, which makes sense since the equation uses a second derivitive, and therefore shifts the waveform by two lots of 90deg.

Am I right?

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