Tests on a gyroscope show that it can withstand any random vibration along a given axis if the frequency content is between 0 and 1,000 rad/sec and the rms acceleration is less than 80 in/see. This gyro is to be mounted in a rocket where it will be subjected to acoustic-pressure-induced vibration. The transfer function between pressure and acceleration and the mean-square spectral density of pressure are as given in below figure 1. Will this gyro withstand the vibration? Vibration acceleration - Gyro in cys (in/sec²)2 rad/sec rad/e A,A, 1.0 as o 30 Output=sin((,- 30 Figure: 1 Output [coste,- eur - cos( + 0,r) 100 50 100 200 12.5 Random loading e(r) 300 400 500 200 +90'] + + sin(x, +, -90'] output spectral density 20 frequency, rad/sec (3.270) 500

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Maxwell speed distribution

Maxwell-Boltzmann distribution or commonly known as Maxwell speed distribution, explains the division of the energy levels of the molecules of an ideal gas on the basis of the statistical theory. In 1859, Scottish physicist James Clerk Maxwell established the context for the distribution of molecular velocities for random molecules moving in a closed environment. This theory was generalized in 1871 by German physicist Ludwig Boltzmann. He improvised the theory to express the distribution of energy levels among different molecules.