Question

The FFT analysis of a vibration signal from a vehicle is to reveal the presence of harmonics when the engine speed is about 600 rpm. It is required to be able to resolve the frequency components with the
resolution corresponding to 3 rpm. The frequency bandwidth of interest is 1000 Hz.
Describe essential requirements that the measurement must meet in order to achieve the stated objective.

Answer 1

yes

Answer 2

its mechanical engineering 2 year calle engineering analysis

Answer 3

Nyquist's sampling theorem requires that, in order to capture a signal of 1000 Hz, we must sample it at a minimum of double that frequency, or 2000 Hz. That's the first piece of information we can determine.

To obtain a frequency resolution of 3 rpm, we first have to calculate the corresponding frequency that 3 rpm produces:

3 cycles/minute * 1 minute/60 sec = 0.05 Hz vibration

Each "bin" or "bar" of an FFT graph has a resolution equal to Fs/N, where Fs is sampling frequency, and N is the number of samples taken.

Fs/N = 3 rpm = 0.05 Hz
2000/N = 0.05
N = 40000

Thus, we need access to 40,000 samples before we can distinguish between two harmonics that differ by 3 rpm. (This means that you'd need to store 20 seconds of vibration data before your requirement is fulfilled.)