1. For the following two-DOF system, determine the first natural frequency usingequation method: Raylieghsm2=2 kgk₂=80 N/mm₁ =1 kgwwwk₁=40 N/m

In this problem, we are given a two degrees of freedom (DOF) system with two masses (m1 and m2) and…

Answered: 1. For the following two-DOF system,…

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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Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6 – 4km²w4 + 3k?mw² = 0 where the value of the mass, m = 0.1 kg and spring stiffness coefficient, k = 10 N/m. By performing your calculation (final answer in 3 decimal points): (a) Determine the most positive roots of the system, w using Bisection Method. Use initial value of [5.7, 15.5]. Iterate until 5th iteration. (b) Determine the most positive roots of the system, w using Secant Method. Use initial value of [5.7, 15.5]. Iterate until 5th iteration c) The exact value of the most positive roots, w is given as 10 rad/s. Based from your answer in Q1(a) and Q1(b), identify its percentage relative error and justify which method is more accurate.

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1. For the following two-DOF system, determine the first natural frequency using equation method: Raylieghs m2=2 kg k₂= 80 N/m m₁ =1 kg www k₁= 40 N/m