An aircraft undercarriage oleo can be simplified to a mass-spring damper system with a single degree of freedom as per figure Q1. The system is underdamped with a damped natural frequency of 1.2 Hz and the ratio between its amplitude of vibration in the first cycle and that after two cycles is 1: 10, i.e., x3 =1. If the system has a X1 10 mass, m = 2500kg, determine: a) The damping ratio. b) The undamped natural frequency. c) The equivalent spring stiffness.

An aircraft undercarriage oleo can be simplified to a mass-spring damper system with a single degree of freedom as per figure Q1. The system is underdamped with a damped natural frequency of 1.2 Hz and the ratio between its amplitude of vibration in the first cycle and that after two cycles is 1: 10, i.e., x3 =1. If the system has a X1 10 mass, m = 2500kg, determine: a) The damping ratio. b) The undamped natural frequency. c) The equivalent spring stiffness.

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

An aircraft undercarriage oleo can be simplified to a mass-spring damper system
with a single degree of freedom as per figure Q1. The system is underdamped with
a damped natural frequency of 1.2 Hz and the ratio between its amplitude of vibration
in the first cycle and that after two cycles is 1: 10, i.e., x3 =1. If the system has a
mass, m = 2500kg, determine:
10
a) The damping ratio.
b) The undamped natural frequency.
c) The equivalent spring stiffness.
d) The critical damping coefficient.
e) The damping coefficient.
www
m
Figure Q1 - Aircraft undercarriage free body diagram.

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