I have a continuous signal $x(t)$ such that
$$x(t)=12\cos(6\pi t)+6\cos(24\pi t)+3\cos(30 \pi t)$$
and is asked to sketch a 1-sided Amplitude Spectrum of the signal $x(t)$ if sampled above the minimum sampling rate.
Because $w=2\pi$, I worked out that the three signals are 3Hz, 12Hz and 15 Hz.
I'm just wondering, when I plot the Amplitude Spectrum should the Amplitude just be the corresponding coefficients? ie. 12 for 3Hz, 6 for 12Hz and 3 for 15Hz?
EDIT: Additionally, what's the difference between 1-sided Amplitude Spectrum and 2-sided Amplitude Spectrum? Does one offer any more benefit over the other?