Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6 - 4km² w+ + 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): (a) Determine the most positive roots of the system, w using Bisection Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. (b) (c) 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. 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].
Q1 The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given as: m³w6 - 4km² w+ + 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): (a) Determine the most positive roots of the system, w using Bisection Method. Use initial value of [4+(0.1*A), 12+(B/2)]. Iterate until 5th iteration. (b) (c) 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. 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].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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NUMERICAL METHOD
USE: A=1
B=10
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