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Finding the period of trig series analytically?

  1. Sep 3, 2011 #1
    Is there a way to calculate the period of a trigonometric series (like the one below) analytically?

    x(t)=5sin(16t)-4cos(8t+3.1)
     
  2. jcsd
  3. Sep 3, 2011 #2

    mathman

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    The period in this case can be gotten from: 8t = 2π or t = π/4. This works since the other term has a period 16t = 2π or t = π/8 which is a harmonic.
     
  4. Sep 3, 2011 #3
    Sorry, I'm still confused. For this example...

    x(t)=4sin(15t)-3cos(9t+1.1)

    ...I have graphed this in MATLAB, and graphically found a period of about 2.1. I am trying to apply what you suggested, but can't figure out how to calculate the period of 2.1...
     

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  5. Sep 3, 2011 #4

    LCKurtz

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    The sum of two periodic functions will be periodic it the two periods are commensurable. That means the ratio of their periods is a rational number. And in that case, the period is the least common multiple of the individual periods. For non-integers p and q, the LCM is the least number z such that ap = z and bq = z for a and b integers.

    .
     
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