Mirror Vibration and Engine RPMs

It will be related, but only insofar as almost anything will resonate at some frequency. So as the enging goes up and down the rev range at some point the mirror and it's supporting structure may well hit resonance. The structure needs to be designed so any resonance is outside the rev range of the engine.
The engine is just acting as a sweep generator producing a range of different frequencies, if you plotted amplitude of mirror vibration vs engine revs it would be an undulating line with maybe one or two huge resonance peaks. No actual linear or geometric correlation.
Del

i didnt logged the engine rpm while conducting the trials i only took readings of the accelerometer at different locations and structures but how can i correalte and find out a conclusion out of it . i collected data on different engine rpms through rpm meter located in the vehicle.

but how can i correalte and find out a conclusion out of it.

Perform a sensible test...like at school...method, results, conclusion.
Like I said ..if you are trying to correlate engine revs and mirror movement you must log the two things against eachother....I'd have thought it was obvious.
didnt logged the engine rpm while conducting the trials
Well you are very naughty...you should go and sit on the naughty step and think about how to perform some useful tests.
Del

The world of mechanical vibration and electronic ac theory are related and you should be be able to source graphs showing output amplitude versus the ratio of exciting frequency of the driver and natural frequency of the driven. This might give you some insight.

A general rule is that a low frequency can excite a higher natural frequency but not the reverse eg. a higher frequency driver will not excite a system with a lower natural frequency. A real life complication is that many/most sources are not a single frequency but the sum of a number of frequencies (see Fourier series of Bessel Function) . For your problem you will be wanting to keep the natural frequency of the external mirror lower than the lowest of the engine sourced frequencies. That and a little damping should do the job.

There's a whole bunch of things you should consider, like condition of the motor supports (rubber blocks), body integrity, body fastening, stiffness of the mirror's arm and it's glass holder.

Also have in mind that a poorly tunned motor will vibrate more.

One thing that will help the motor run noticeable smoother is the use of an MSD (Multiple Spark Discharge) module, it quadruples the voltage to the coil and gives six consecutive Hi-Volt discharges to each spark plug within its explosion time.

Yahlasit

the relation betwen mirror and ths rpm machine are the resonance, frecuency in rpm is equal to frecuency natural the mirror and this change, when you changing the mass the mirror or the suport