# A single cylinder oil engine works with a three rotor system, the shaft length is 2.5m and 70mm in diameter, the middle rotor is at a distance 1.5m from one end. Calculate the free torsional vibration frequency for a two node system in Hz if the mass moment of inertia of rotors in Kg-m^2 are: 0.15, 0.3 and 0.09. C=84 kN/mm^2

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A single cylinder oil engine works with a three rotor system, the shaft length is 2.5m and 70mm in diameter, the middle rotor is at a distance 1.5m from one end. Calculate the free torsional vibration frequency for a two node system in Hz if the mass moment of inertia of rotors in Kg-m^2 are: 0.15, 0.3 and 0.09. C=84 kN/mm^2

(a) 257

(b) 281

(c) 197

(d) 277

I have been asked this question in semester exam.

I want to ask this question from Torsionally Equivalent Shaft in portion Torsional Vibrations of Machine Dynamics

by (38.6k points)
The correct option is (d) 277

Explanation: For a two node system, the first node occurs at a distance 0.4356 m from left end.

The polar moment of inertia = 2.36×10^6 m^4

La = 0.4356m ( from same frequency relation )

Lc = 0.726 m

Substituting these values into the frequency relation we get

f = 277 Hz.

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