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Average of a sinusodial Function

  1. Sep 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the average of a sinusoidal function over 1.5 cycles

    2880*sin(wt - 30 degrees)

    2. Relevant equations


    3. The attempt at a solution

    Alright so

    1/( (3*pi)/2 - 0) * integral[0, (3*pi)/2] 2880*sin(wt - 30 degrees) dt
    I shift it over to the origin because it shouldn't effect the average no matter the phase?
    (5760/(3pi)) * integral[0, (3*pi)/2] 2880*sin(wt) dt
    - (5760/(3pi))*cos(t)|[0, (3*pi)/2]
    - (5760/(3pi))*(0-1)
    1920/pi

    Does this look ok?
     
  2. jcsd
  3. Sep 14, 2015 #2

    berkeman

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    Staff: Mentor

    That doesn't sound right to me. 1.5 cycles means 1 cycle which averages to zero, but then the other 1/2 cycle can be either positive or negative, which give very different averages.

    Are you sure you are writing out the whole problem? Is a t=0 start specified?
     
  4. Sep 14, 2015 #3

    epenguin

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    Homework Helper
    Gold Member

    Quote: Does this look ok?

    Even if it was OK you can't say it looks OK . I recently found it is not all that hard to use Tex for integrals and is only way for them to look presentable.

    But are you sure one and a half cycles is 3π/2 ?

    I don't think your answer should have π in the answer, I mean does sin(π) or sin or cos of any easy fraction of π have it?

    Optionally simplify by the thought that
    one and a half is, er,
    One... :oldwink:
    and a half.

    I don't think it's right that the thing is not changed by phase though it was tempting to think so. Because some of a half-cycle is positive and some negative, and as you change phase some of the positive is becoming negative with no compensation.

    I suggest you draw yourself a picture of this sine and its limits and you will see this.
     
    Last edited: Sep 15, 2015
  5. Sep 14, 2015 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Questions:
    (1) Why do you choose an upper limit of 3*pi/2? What happened to w?
    (2) Are you really sure that you can shift the origin? Certainly, for a whole number of cycles you could do it, but have you actually proven that you can do it for a fractional number of cycles?

    Anyway, my answer does not agree with yours.

    Finally: never mix up units the way you are doing; either use degrees all the way, or radians throughout--with the latter strongly preferred, as it makes integration and differentiation easier. So, re-write 30 degrees in terms of radians.
     
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