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## Homework Statement

The input signal of a first-order lowpass filter with a transfer function given by eqn 1 below and a half power frequency of 200 Hz is eqn 2 below. Find an expression for V_out

## Homework Equations

eqn1:

H(f) = 1/(1+j*(f/f_B) where f is the frequency and f_B is the half-power frequency

eqn2:

v_in (t) = 3 + 2sin(800*PI*t + 30) + 5cos(20000*PI*t)

v_out/v_in = H(f)

## The Attempt at a Solution

I have already gotten that v_in = 3 + 2cos(800*PI*t - 60) + 5cos(20000*PI*t)

then I would multiply each component by H(f) which will give me:

H(400) = 1/sqrt(5) phase(-arctan(2))

H(1000) = 1/sqrt(26) phase(-arctan(5))

v_out = 3*H(?) + 2 phase(-60)*H(400) + 5 phase(0)*H(1000)

pretty much I just do not know what I do about the 3. Do I simply leave it alone?

Thanks!

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