A vibration model of a machine system that consists of three levers connected by lightweight linkages (represented by spring) is shown in Figure Q1. Each lever has a length, L with the distance of linkage from pivot point is given as 'a'. Important: Please provide the final answer equation of motion in the matrix form of unknown m, k, a and L. (a) By using Lagrange equation, determine the equation of motion of the system by considering 01, 02 and 03 are very small. (b) Prove the answer from Q1(a) by using Newton's second law. Use a free body diagram to support the answer.

A vibration model of a machine system that consists of three levers connected by lightweight linkages (represented by spring) is shown in Figure Q1. Each lever has a length, L with the distance of linkage from pivot point is given as 'a'. Important: Please provide the final answer equation of motion in the matrix form of unknown m, k, a and L. (a) By using Lagrange equation, determine the equation of motion of the system by considering 01, 02 and 03 are very small. (b) Prove the answer from Q1(a) by using Newton's second law. Use a free body diagram to support the answer.

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 vibration model of a machine system that consists of three levers connected by
lightweight linkages (represented by spring) is shown in Figure Q1. Each lever has a
length, L with the distance of linkage from pivot point is given as 'a'.
Important: Please provide the final answer equation of motion in the matrix form of
unknown m, k, a and L.
(a)
By using Lagrange equation, determine the equation of motion of the system
by considering 01, 02 and 03 are very small.
Prove the answer from Q1(a) by using Newton's second law. Use a free body
(b)
diagram to support the answer.

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