Help converting voltage to complex number

Discussion in 'Homework Help' started by justmonkey23, Nov 8, 2009.

  1. justmonkey23

    Thread Starter New Member

    Nov 8, 2009
    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?
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    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?
  3. justmonkey23

    Thread Starter New Member

    Nov 8, 2009
    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:

    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.
  4. Thav


    Oct 13, 2009
    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).