20*pi is correct.
It makes sense because 40*pi is it's 2nd harmonic and 60*pi the 3rd.
Try and plot both your function and cos(20*pi*t) and you'll see they have the same repetition period.
You don't have to believe to anyone's theory, just fire up Matlab/excel, plot it and measure the repetition period.
You should find 10Hz:
cos(20*pi*t) = cos(10 * 2*pi*t) -> 10 Hz
cos(40*pi*t) = cos(20 * 2*pi*t) -> 20 Hz
cos(60*pi*t) = cos(30 * 2*pi*t) -> 30 Hz
First of all the frequency is w/2Pi in the equation x(t)=VpSin(wt+o)
Secondly, the fundamental frequency is the smallest frequency by which all other harmonic frequencies are integer multiples of.
Note, the fundamental frequency does not necessarily exist in the transform. ie: it could be filtered out.
So, Dave's second answer of 10 is correct.
40 Pi t = 2 x wt
60 Pi t = 3 x wt
120 Pi t = 6 x wt
where w=2 Pi f
and f=10
The fundamental frequency of 10 is absent but 20 is incorrect because then 60 w t would equal 1.5 times the fundamental which is not part of a Fourier transform.
40 is even more incorrect because w=2 x Pi x f not just Pi x f plus it is not an integer of the fundamental.
I gave twice the same answer, because cos(20*pi*t) is a signal at 10Hz.
Just remember that you need 2*pi to complet a period, so cos(F * 2 * pi * t) is a signal at F Hz.
Hope it is more clear now ...
You originally asked for the fundamental frequency. It is 10.
w=2*Pi*f = 20 * Pi - this is the angular frequency.
What is the question actually asking for? angular frequency or frequency? There is an important distinction!
If the choices of answers are in multiples of Pi then it should be asking for angular frequency ( also radian frequency ).
Note: the importance is not to get the answer correct, it is to understand the concept. How else will you answer the question on a final exam?