How do you find Vout(t) from Vin(t) and the transfer function?

[Equalizer]

Homework Statement

Suppose Vin(t) = 4cos(2pi*t + 20*) + 3cos(4pi*t + 30*) +5sin(5pi + 50*)V and Vin(t) passes through a system with the following transfer function characteristic H(f):
|H(f)| = 10f + 1 (magnitude response with f in Hz)
<H(f) = (5*)f (phase response)

Find V_0(t) of this system as Vin(t) is passed through it.

Homework Equations

H(f) = Vout(t) / Vin(t)
H(f) = 1 / (1+j(f/f_b))
|H(f)| = 1 / sqrt(1 + (f/f_b)^2)
<H(f) = -arctan(f/f_b)

The Attempt at a Solution

I broke Vin(t) into 3 separate terms and found the polar form of each, as well as the particular value for f

V1 = 4<20*, f1 = 2pi/2pi = 1
V2 = 3<30*, f2 = 4pi/2pi = 2
V3 = 1.31<0*,f3 = 0/2pi = 0

From how I interpret the problem, the statement has a typo and is actually asking for Vout(t). So,

Vout(t) = H(f)*Vin(t)
Vout(t) = H(f1)*V1 + H(f2)*V2 + H(f3)*V3

My problems seems to be that I can not get H(f) from |H(f)| and <H(f). No graph is given. Any advice? Thanks in advance!

 

[p1ayaone1]

Vout(t) = H(f)*Vin(t)

careful: you can't compare apples and oranges. You just need to put Vin in the frequency domain. You have H(f) though:

H(f) = 1 / (1+j(f/f_b))

now Vout(f) = H(f)*Vin(f) becomes a problem of doing the inverse transform back to the time domain.