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Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6 – 4km²aw4 + 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): Determine the most positive roots of the system, wusing Bisection Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. (a) (b) Determine the most positive roots of the system, w using Secant Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. 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. (c)

Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6 – 4km²aw4 + 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): Determine the most positive roots of the system, wusing Bisection Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. (a) (b) Determine the most positive roots of the system, w using Secant Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. 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. (c)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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USE A=1

B=8

Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6 – 4km²w4 + 3k²mw² = 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): (а) Determine the most positive roots of the system, wusing Bisection Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. (b) Determine the most positive roots of the system, w using Secant Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. 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. (c) NOTE: A is the 5th digit of your matric number and B is the 6th digit of your matric number. If happen to be the 5th or 6th digit of your matric number (A or B) = 0, take 10 as the replacement value. Do not use 0 number. For example, if your matric number is AD070102, use A = 10 and B= 2 and the initial value would be [5, 13].
Transcribed Image Text:Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6 – 4km²w4 + 3k²mw² = 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): (а) Determine the most positive roots of the system, wusing Bisection Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. (b) Determine the most positive roots of the system, w using Secant Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. 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. (c) NOTE: A is the 5th digit of your matric number and B is the 6th digit of your matric number. If happen to be the 5th or 6th digit of your matric number (A or B) = 0, take 10 as the replacement value. Do not use 0 number. For example, if your matric number is AD070102, use A = 10 and B= 2 and the initial value would be [5, 13].
X2 k2 X3 X1 m2 m3 Figure Q1
Transcribed Image Text:X2 k2 X3 X1 m2 m3 Figure Q1
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