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Homework Help: Sinusoidal Waveforms

  1. Sep 16, 2007 #1
    1. The problem statement, all variables and given/known data

    Could you please help me decide on these answers?
    The question is " Are the following statements Sinusoidal? And are they Periodic?
    I have produced the waveforms in MathCad
    The limits are 0 - 4Pi

    1.f(x)= sinx + 2sin(x-(Pi/6))
    2.f(x)= sinx +sin2x
    3.f(x)= sinx + 1/2(sin2x)
    4.f(x)= sinx + 1/3(sin3x)+1/5(sin5x)
    5.f(x)= sinx.cos2x
    6.f(x)= sin3x.sin2x
    7.f(x)= sin^23x
    2. Relevant equations

    3. The attempt at a solution

    I think they are all periodic as my understanding of periodic is that the waveform repeats itself after 2pi (360 degrees) Which they all seem to do.
    I am unsure about the Sinusoidal part though. I know that number 1 is but not sure about the rest!! How do I tell?

    I also have to work out the r.m.s value of a complex waveform, Am I right in saying that if its sinusoidal I can use Vmax/root2? If its not sinusoidal can I use this formula?

    Last edited: Sep 16, 2007
  2. jcsd
  3. Sep 16, 2007 #2


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    Staff Emeritus
    Science Advisor

    Periodic means that the function repeats the same value 'periodically', i.e. with the same period, i.e. f(t) = f(t+T) = f(t+nT) where n is an integer, and T is the period.

    Integating the sin function over one period gives 0.

    See - http://en.wikipedia.org/wiki/Sine_wave

    A sinusoidal function certainly is one that can be put in the general form

    [tex] y(t) = sin (\omega t + \theta) [/tex], where [itex]\omega[/itex] is the angular frequency (rad/sec) = 2[itex]\pi[/itex] f, and [itex]\theta[/itex] is the phase or phase shift in radians.
  4. Sep 16, 2007 #3

    Thanks for the reply. I get the periodic part now (Many Thanks)

    However I am still somewhat confused about the Sinusoidal part. All the formulas mention Time or frequency, however I only seem to have a phase figure. (i.e) I have 0 - 4Pi plotted along the horizontal axis and Amplitude along the vertical axis in my graphs.

    Am I missing something blindingly obvious?

    Many Thanks
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