Sampling frequency, Fs = 2 kHz --> dt = 1/Fs
Fmax = 1/2dt --> Fs/2 --> Fmax = 1 kHz
The signal is sampled such that baseband FFT will have frequency of 0-1 kHz. You may only be interested in 0-120 Hz because that's where all the action is in the signal, but you'll have calculated 0-1 kHz. Matlab doesn't have a builtin zoom FFT; you'll just need to only take the section of the result of interest.
See doc fft for example of one-sided PSD from time signal; significant points using your variables would be
Fs = 2000;
T = 1/Fs;
L = numel(time);
y = fft(timeSeries);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
posFreq = Fs*(0:(L/2))/L;
From your information above, presuming it is correct, with Fs=2000 and L=20000; then we'll find that
>> [f(1) f(end)]
as we suspected early on. Also, then
So, to keep the first 120 Hz of the PSD, need 120/df --> 1200 elements.
I have no idea what you intend by the statement "My ultimate goal is to have a frequency by time plot."
The entire time series is converted in the FFT so the frequency is the content of the entire waveform. If you intend to look at some portion of the time signal and compare a given peak or somesuch, then you would have to process the time series over the desired time sections and compare those results.