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## Homework Statement

For a RLC circuit with RC = 1/2 and LC = 1/16 determine the differential equation that describes the relationship between the input and output voltages. An image of the circuit is shown with RLC all in series with the input voltage Vi(t) across all 3 components. The voltage drop across the capacitor is labelled Vo(t)

## Homework Equations

Kirchoff's Voltage Law

## The Attempt at a Solution

From Kirchoff's voltage law:

Vi(t) = Vr(t) + Vc(t) + Vl(t)

Vr(t) = Rir(t) = RC(Vc(t))' = RC(Vo(t))' Using the prime to indicate differentiation

The voltage drop across the resistor can now be descirbed as above henceforth we now have:

Vi(t) = RC(Vo(t))' + Vc(t) + Vl(t)

Given that Vc(t) = Vo(t) we can also write:

Vi(t) = RC(Vo(t))' + Vo(t) + Vl(t)

The voltage drop across the inductor can be expressed as:

Vl(t) = L(il(t))' and as ir = ic = il Vl(t) = LC(Vo(t))'

Henceforth the differential equation is:

Vi(t) = RC(Vo(t))' + Vo(t) + LC(Vo(t))'

Is this solution correct or have I flamingo'd up somewhere?

## Homework Statement

## Homework Equations

## The Attempt at a Solution

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