Harmonics and fundamental frequency questions

[esmeco]

I'm having a bit of a difficulty trying to determine the fundamental frequency in a given function and the harmonics.
In the equation below,would the fundamental frequention be 1 (corresponding to the value cos(1x-pi)) and the harmonics amplitude 3 and -4?Also,the values of the frequency of the harmonic are equal (both 3),so how would it be represented in the domain frequency?

Considering x=w0t

v(t)=3sin(3x) - 4cos(3x) + cos(x-pi)

cos(x-pi)=cosx (is this right??),so

v(t)=3sin(3x) - 4cos(3x) + cos(x)


Thanks in advance for the reply!

 

[HallsofIvy]

I'm having a bit of a difficulty trying to determine the fundamental frequency in a given function and the harmonics.
In the equation below,would the fundamental frequention be 1 (corresponding to the value cos(1x-pi)) and the harmonics amplitude 3 and -4?Also,the values of the frequency of the harmonic are equal (both 3),so how would it be represented in the domain frequency?

Considering x=w0t

v(t)=3sin(3x) - 4cos(3x) + cos(x-pi)

cos(x-pi)=cosx (is this right??),

No, it's not right.
In particular, if x= pi, cos(pi-pi)= cos(0)= 1 but cos(pi)= -1.
What is true is that cos(x- pi)= -cos(x).

so

v(t)=3sin(3x) - 4cos(3x) + cos(x)


Thanks in advance for the reply!

 

[esmeco]

...

So,conseidering what you've said,the equation would be:

v(t)=3sin(3x) - 4cos(3x) - cos(x)

And what about what this:

In the equation below,would the fundamental frequention be 1 (corresponding to the value cos(1x-pi)) and the harmonics amplitude 3 and -4?Also,the values of the frequency of the harmonic are equal (both 3),so how would it be represented in the domain frequency?

Am i right?