# 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

## The Attempt at a Solution

need a hint ..

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NascentOxygen
Staff Emeritus
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
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