1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Stuck on proving that this function\signal is not periodic

  1. Dec 2, 2009 #1
    First of all, HI! This is my first post and my first day in this forum. =)

    I am having quite a problem demystifying this function. It's on a book I have and it clearly states that it isn't periodical. I can't reach that conclusion and was hoping you could help me out.

    So, the function in question is [tex]x(t)=sin(\pi t)cos(10t)[/tex]

    What I did was to deconstruct this into
    [tex]\frac{1}{2}\left[ sin(\pi t+10t)-sin(\pi t-10t)\right][/tex]

    Now, I think that the period of the first sin is [tex]\frac{2\pi}{\pi +10}[/tex] and the one from the second sin is [tex]\frac{2\pi}{\pi -10}[/tex].

    I then try to find the fundamental period of the whole function:

    [tex]n\frac{2\pi}{\pi +10}=m\frac{2\pi}{\pi -10}\Rightarrow m=\pi -10[/tex] and [tex]n=\pi+10 \Rightarrow T=2\pi[/tex]

    I know I have to be doing something wrong and possibly it's also really basic, but I got stuck.
    Can anyone help me out? =)
  2. jcsd
  3. Dec 3, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    But your m and n aren't integers. Try an indirect argument. Suppose your x(t) has period P, so x(t+P) = x(t). What does that give you? What happens if you put t = 0 in it?
  4. Dec 3, 2009 #3

    I had done the substitution before, and noticed it didn't work, but couldn't understand why.
    As soon as you said "integer" however, I just facepalmed myself.

    Thank you so much.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook