I am trying to convert my voltage given as x(t) = 50 sin( 10 t) + 50 sin (20 t) to a complex number. I believe if I only had x(t) = 50 sin( 10 t) then my answer would be just 50 +0j. How do I use that second sin function? is it just 50+50j?

 

As far as I know you can only convert in one frequency base (at a time) to the complex domain - you can't do it for two (or more) frequencies.

Who set this problem?

 

The circuit below is given: R1=10 Ohms, L1=L2=5 Henry and C=0.01 Farads.
Suppose the input voltage x(t) = 50 sin( 10 t) + 50 sin (20 t)


5.1 Derive y(t) for problem 1.

Seems diagram would not link well so:
http://benbuschmann.com/set7a.pdf

My plan was to convert the voltage to complex numbers then use a section in volume II on this site to work through the problem. I have H(s) for this worked out as well if that makes things easier.

 

So x(t) is your input voltage, are you asked to give the output voltage in terms of a complex number? If not I think you can use superposition to get the output voltage as a function of t.

That is, consider x1(t) to be 50*sin(10*t), w=10, find your output through H(s) and convert back to y1(t), then do the same with x2(t) = 50*sin(20*t), w=20 and get y2(t). You can then add y1(t) and y2(t) to get y(t).