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Find fundamental period of x(t) = cos(Pi * t)

  1. Aug 29, 2007 #1
    1. The problem statement, all variables and given/known data

    Find fundamental period of [tex]x(t)\,=\,cos\left(\pi\,t\right)[/tex]



    2. Relevant equations

    [tex]x(t)\,=\,A\,sin\left(\omega_0\,t\,+\,\phi\right)[/tex]

    Which has a fundamental period [tex]T\,=\,\frac{2\pi}{\omega_0}[/tex]



    3. The attempt at a solution

    [tex]\omega_0\,=\,\pi[/tex] <---- Right?

    [tex]T\,=\,\frac{2\pi}{\pi}\,=\,2[/tex]

    [tex]T\,=\,2[/tex]
     
  2. jcsd
  3. Aug 29, 2007 #2

    dextercioby

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    T=2 s. Don't forget the units.
     
  4. Aug 29, 2007 #3

    HallsofIvy

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    "s"? What is "s"? The problem, as stated, does not have units- it is a pure function. Even if you assume "t" is time (I would not, I see no reason to assume this is a physics problem rather than a mathematics problem) why would you assume the units are seconds rather than minutes or hours?

    In any case, VinnyCee, your analysis is correct.
     
  5. Aug 29, 2007 #4
    Thanks for your help!

    So, are the following correct?

    [tex]x(t)\,=\,cos\left(3\,\pi\,t\right)\,\,\longrightarrow\,\,\omega_0\,=\,3\,\pi\,\,\longrightarrow\,\,T\,=\,\frac{2\,\pi}{3\,\pi}\,=\,\frac{2}{3}[/tex]

    [tex]x(t)\,=\,sin\left(4\,\pi\,t\right)\,\,\longrightarrow\,\,\omega_0\,=\,4\,\pi\,\,\longrightarrow\,\,T\,=\,\frac{2\,\pi}{4\,\pi}\,=\,\frac{1}{2}[/tex]

    [tex]x(t)\,=\,cos\left(\frac{\pi}{2}\,t\right)\,\,\longrightarrow\,\,\omega_0\,=\,\frac{\pi}{2}\,\,\longrightarrow\,\,T\,=\,\frac{2\,\pi}{\frac{\pi}{2}}\,=\,\frac{4\,\pi}{\pi}\,=\,4[/tex]

    [tex]x(t)\,=\,sin\left(\frac{\pi}{3}\,t\right)\,\,\longrightarrow\,\,\omega_0\,=\,\frac{\pi}{3}\,\,\longrightarrow\,\,T\,=\,\frac{2\,\pi}{\frac{\pi}{3}}\,=\,\frac{6\,\pi}{\pi}\,=\,6[/tex]
     
  6. Aug 29, 2007 #5

    HallsofIvy

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    Yes.
     
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