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Harmonic function. vibration

  1. Jan 11, 2015 #1
    1. The problem statement, all variables and given/known data

    three harmonic function of frequency p, 2p ,3p were added together. what is the frequency of resultant periodic function?
    2. Relevant equations
    X=Asin(wt)
    A-amplitude w-frequency
    X=X1+X2+X3

    3. The attempt at a solution
    need a hint ..
     
  2. jcsd
  3. Jan 11, 2015 #2

    NascentOxygen

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    Staff: Mentor

    You could try sketching the 3 sinusoids, and then adding them graphically. Sum 2 first, then to that add the third, and look for the period of the resultant.

    But I think you should be able to do this mathematically. Do you have an equation from trigonometry:
    sin A + sin B = ......
     
  4. Jan 11, 2015 #3
    yes sir but I dont hv known limits in Grapically ..only freq . so by trignometricaL relation i tried it( as u said) ..with sin A+sinB=(1/2)*sin((1/2)(A+b))*Cos((1/2)(A-B)). . i get in the form sin*cos+Sin(C)
    AND no use of sin A*cosB.. how to proceed here
     
  5. Jan 11, 2015 #4
    resultant frequency X=p. Any IDEA how they got it
     
  6. Jan 11, 2015 #5

    NascentOxygen

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    Staff: Mentor

    now let B=2A when you are summing a frequency with its double frequency
     
  7. Jan 11, 2015 #6

    NascentOxygen

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    Staff: Mentor

    So, you plot for just a few cycles. Periodic waveforms are repetitive, what happens during one period also happens during the next period, so you just need to discover the period, and shape of waveform for one cycle.
     
  8. Jan 11, 2015 #7
    thanks Nas .. i got the solution...sinusoids having frequencies in integer multiple of (f) have net freq (f) when addded together..when i consider by t=1/f ..its pretty clear final net freq occur only after first signal ..so answer is P
     
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