# Harmonic function. vibration

## Homework Statement

three harmonic function of frequency p, 2p ,3p were added together. what is the frequency of resultant periodic function?

## Homework Equations

X=Asin(wt)
A-amplitude w-frequency
X=X1+X2+X3

need a hint ..

## Answers and Replies

NascentOxygen
Staff Emeritus
Science Advisor
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 = ......

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

resultant frequency X=p. Any IDEA how they got it

NascentOxygen
Staff Emeritus
Science Advisor
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))
now let B=2A when you are summing a frequency with its double frequency

NascentOxygen
Staff Emeritus
Science Advisor
yes sir but I dont hv known limits in Grapically ..only freq
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.

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