Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6 – 4km²wª + 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.

Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6 – 4km²wª + 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.

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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Properties of Pure Substances

A substance with fixed chemical composition throughout is called a pure substance like water, air, and nitrogen. A pure substance does not have to be a single element or compound. A mixture of two or more phases of a pure substance is also a pure substance as long as the chemical composition is the same for all phases. These substances mainly have a constant/ uniform composition. The substances also have fixed boiling and melting points. A pure substance takes part in a chemical reaction to form predictable products.

Question

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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