A single cylinder vertical petrol engine of total mass 320 kg is mounted upon a steel chassis and causes a vertical static deflection of 2 mm. The reciprocating parts of the engine have a mass of 24 kg and move through a vertical stroke of 150 mm with simple harmonic motion. A dashpot attached to the system offers a resistance of 490 N at a velocity of 0.3 m/sec. Determine: (i) The speed of the driving shaft at resonance; (ii) The amplitude of steady state vibration when the driving shaft of the engine rotates at 480 rpm.

A single cylinder vertical petrol engine of total mass 320 kg is mounted upon a steel chassis and causes a vertical static deflection of 2 mm. The reciprocating parts of the engine have a mass of 24 kg and move through a vertical stroke of 150 mm with simple harmonic motion. A dashpot attached to the system offers a resistance of 490 N at a velocity of 0.3 m/sec. Determine: (i) The speed of the driving shaft at resonance; (ii) The amplitude of steady state vibration when the driving shaft of the engine rotates at 480 rpm.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

(a)
A single cylinder vertical petrol engine of total mass 320 kg is mounted upon a steel
chassis and causes a vertical static deflection of 2 mm. The reciprocating parts of the
engine have a mass of 24 kg and move through a vertical stroke of 150 mm with
simple harmonic motion. A dashpot attached to the system offers a resistance of 490
N at a velocity of 0.3 m/sec. Determine:
(i) The speed of the driving shaft at resonance;
(ii) The amplitude of steady state vibration when the driving shaft of the engine
rotates at 480 rpm.
(b) A vibrating system is defined by the following parameters:
m=3 kg, k = 100 N/m, C=3 N-sec/m
Determine
(i) the damping factor,
(ii) the natural frequency of damped vibration,
(iii) logarithmic decrement,
(iv) the ratio of two consecutive amplitudes and
(v) the number of cycles after which the original amplitude is reduced to 20
percent.

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