How to calculate the magnitude of a function?

  1. 1. The problem statement, all variables and given/known data
    I have this function:

    G(w)=[itex]\frac{1}{j\omega\tau+1}[/itex]
    I want to find the magnitude

    2. Relevant equations
    S=[itex]\alpha[/itex]+j[itex]\beta[/itex]

    magnitude(S)=[itex]\sqrt{[itex]\alpha[/itex]^{2}+[itex]\beta[/itex]^{2}}[/itex]


    3. The attempt at a solution[/b

    What i did was carry out the division,

    so i got
    [itex]\frac{j\omega\tau-1}{-(j\omega+1)}[/itex]
    then do i just split it into real and imaginary part and then take the magnitude using this?
    S=[itex]\alpha[/itex]+j[itex]\beta[/itex]

    magnitude(S)=[itex]\sqrt{[itex]\alpha[/itex]^{2}+[itex]\beta[/itex]^{2}}[/itex]

    Can anyone help i am not so sure how to approach this?
     
  2. jcsd
  3. This is where you got it wrong. Try to multiply the numerator and the denominator of the original G(ω) by [itex] - j ω \tau + 1[/itex] and see what you get.
     
  4. Then, try and think what you had to multiply by the expression [itex]- j ω \tau + 1 [/itex] to get your answer.
     
  5. Ray Vickson

    Ray Vickson 6,305
    Science Advisor
    Homework Helper



    Failexam's suggestions are all you need to do. However, if you are going to use LaTeX, why not do it properly? Your expression for "magnitude(S)" is ugly; here is what it should look like: [itex]\text{magnitude}(S)=\sqrt{\alpha^2 + \beta^2}.[/itex] To get this, just remove the "inner" [i t e x]-[/i t e x] pairs; furthermore, if you want the word "magnitude" to appear in nice text font, just include it inside the [i t e x] command, but say \text{magnitude}.

    RGV
     
  6. The magnitude of two vectors divided is the division of the magnitudes. What is the magnitude of the numerator? What is the magnitude of the denominator? What is the result of dividing those magnitudes?
     
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