I have just completed an assignment on sampling theory where I had to model a wave which was made up of the sum of two waves the second being twice the frequency of the first. I then had to use the fourier transform in excel to get a spectral density function. The amplitude of the waves was a measure of displacement.

I now have to answer a couple of questions related to the assignment which I am struggling with (I am a structural Eng. student rater than a maths student ). I hope somebody can point me in the right direction.

1) The time dependent record was in units of metres what units would be on the Y axis of the SDF. What would the units be if the time dependent record was measured in M/sec

I squared the modulus of the spec density function. I think the units are m^2/Hz but I dont know why!!

2) why is using an accelerometer to measure vibration the preffered method of finding displacement.

3) Why does a spectral analysis give a dominant signal at one frequency

4)Why does the number of samples need to be a power of 2. ( I chose 0-255 samples) As I think the FFT in excel needs a power of 2 to work but I dont know why.