Determine the most positive roots of the system, w using Bisection Method. Use initial value of [4+(0.1*10), 12+(10/2)]. Iterate until 5th iteration. Determine the most positive roots of the system, w using Secant Method. Use initial value of [4+(0.1*10), 12+(10/2)]. Iterate until 5th iteration. (b) 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.
Determine the most positive roots of the system, w using Bisection Method. Use initial value of [4+(0.1*10), 12+(10/2)]. Iterate until 5th iteration. Determine the most positive roots of the system, w using Secant Method. Use initial value of [4+(0.1*10), 12+(10/2)]. Iterate until 5th iteration. (b) 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.
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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Question
numerical method
![Q1
The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given
as:
4km?w + 3k2mw? = 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*10), 12+(10/2)]. Iterate until 5th iteration.
(b)
Determine the most positive roots of the system, w using Secant Method. Use initial
value of [4+(0.1*10), 12+(10/2)]. 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.
+ x3
ki
k2
m2
m3
Figure Q1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9126547c-acd1-40cf-b247-1dea65405f3b%2F056d2d7a-c8fb-4821-9f54-681cf113d62f%2F1lxuwqf_processed.png&w=3840&q=75)
Transcribed Image Text:Q1
The frequency equation of a 3 Degree of Freedom spring mass system (Figure Q1) is given
as:
4km?w + 3k2mw? = 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*10), 12+(10/2)]. Iterate until 5th iteration.
(b)
Determine the most positive roots of the system, w using Secant Method. Use initial
value of [4+(0.1*10), 12+(10/2)]. 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.
+ x3
ki
k2
m2
m3
Figure Q1
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