Frequency analysis to determine low-pass cut off frequency I collected some data for a practical application, where the signal represents force data obtained from an impact of a punch against a force plate attached to a quasi-rigid rig (it moves once the impact occurs). I have a few questions to understand how to deal with my data.

Features of the signal:

the signal (sampling 1000Hz) has a length of 2 seconds, but the impact last about 60ms. The recording is 2s for practical reasons though. Therefore, before the impact a baseline is recorded (values close to zero), and after the impact vibrations occur until data set back to baseline levels. I need to figure out a reasonable cut-off frequency to use combined with a 4th order butterworth filter to properly filter the signal.


When exploring (FFT) the frequency of that signal should I use the whole 5s long signal or only the 30ms of interest? Due to sampling frequency, data points over 30ms maybe not enough?
Vibrations occurring due to the impact are not of interest, but the frequency is likely to be in part similar to the frequency of the portion of the signal of interest. How to deal with this? I could select from before the impact (arbitrary) to when the signal becomes zero after the impact. Then use from that point onwards to explore frequency of the unwanted signal only?
Impacts are at least 10 per subject, when exploring the frequency of that signal, should I average all trials and all subjects out to obtain an average frequency content or should I perform the analysis for each trial and subject indepedently?


Attached a figure of a typical signal (x = time; y = Newtons)
I think you will get almost the same amount of frequency content for both the cases (fft of 60 ms and fft of 2 sec). The time series indicates that only from 0.6 to 1.2 sec there is vibration. But it's better to use the full signal while doing the FFT as there is no fear of losing any data. If you cut some portion from the time series, you have to be careful about choosing the window (use cosine tapering not rectangular window) as edging effect may be introduced into your frequency content. 
Sorry, I didn't get the question. Could you please rephrase it?
I think that for all the trials, the time series would be different. Therefore, it is not recommended to average all the time series. It is better to analyze all the time sequences and obtain the frequency contents. If dominant frequencies for all the trials are similar, then the average frequency can be calculated. If not, you can try to find out the reason e.g. inconsistency in the sample material etc.