Consider a mass-spring system shown below. X1 m The system model is given by m 1 2 k₁ 00000 d₁2 m₁ d²x ₂ dt² ² + (k ₂ + k ₂ ) x ₂ − k ₂ x ₂ =F₁(t) k₂ -oooo0 F₁ −k₂x₁ + (k₂+kz) x₂= F₂(1) *2 (1₂²+k;,**₂)) (m₁s²+k₁+k₂) (m ₂s ²+k ₂+k3) −k² (m₁ x ² + (m₁s²+k₁+ where F₁(t) and F₂(t) are the inputs to the system. Find the transfer function X₂(s)/F₁(s). k₂+ką (m₁x² + k₂ +k₂) (m₂x² +k ₂+k₂)—k} (m₁s²+k₁ + k₂) 1 ₁ + k²₂) (m₂x² + ₂+ k₂) - A{ ·k, 1 k₁+k₂ (m₁s²+k₁+k₂) (m₂s² +k ₂+k3) −k² k 3 (m₁s²+k₁+k₂) (m₂s²+k₂+k₂) −k² m₂ (m₂x²+k₂+k₂) k, (m₁s² + k₂ + k₂) (m₂x²³+k₂+k₂) −k² k3 ooood F₂

Consider a mass-spring system shown below. X1 m The system model is given by m 1 2 k₁ 00000 d₁2 m₁ d²x ₂ dt² ² + (k ₂ + k ₂ ) x ₂ − k ₂ x ₂ =F₁(t) k₂ -oooo0 F₁ −k₂x₁ + (k₂+kz) x₂= F₂(1) *2 (1₂²+k;,**₂)) (m₁s²+k₁+k₂) (m ₂s ²+k ₂+k3) −k² (m₁ x ² + (m₁s²+k₁+ where F₁(t) and F₂(t) are the inputs to the system. Find the transfer function X₂(s)/F₁(s). k₂+ką (m₁x² + k₂ +k₂) (m₂x² +k ₂+k₂)—k} (m₁s²+k₁ + k₂) 1 ₁ + k²₂) (m₂x² + ₂+ k₂) - A{ ·k, 1 k₁+k₂ (m₁s²+k₁+k₂) (m₂s² +k ₂+k3) −k² k 3 (m₁s²+k₁+k₂) (m₂s²+k₂+k₂) −k² m₂ (m₂x²+k₂+k₂) k, (m₁s² + k₂ + k₂) (m₂x²³+k₂+k₂) −k² k3 ooood F₂

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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Question

Consider a mass-spring system shown below.
X1
m
k₁
ooooo
The system model is given by
d²x
m
m₁
1 d1²
dx,
2 di²
1
· + (k₁₂ + k₂) x ₂ −k ₂x₂=F₁ (1)
1
k₂
ooooo
F₁
k₂x₂ + (k₂ + k ₂) x₂ = F₂(t)
k₂ +k z
2
m_s
(m_s²³ + k₁+k₂
²+k₁ + k ₂ ) ( m ₂s ² + k₂ + k ₂) -k
2
where F₁(t) and F₂(t) are the inputs to the system. Find the transfer function X₁(s)/F₁(s).
k ₂
(m₁s²+k₁+k₂) (m₂s² + k ₂2 +k₂ ) − k²/
2
₁s² + k ₁+k₂)
1
(m₂x²+₁+k₂) (m₂x²+k₂+^₂)=R}
2 ) ( m²₂ s² + k₂ + k ₂
1
2
m₂
k ₁+k₂
1
(m₁s²+k₁ + k₂) (m₂s² + k₂ + k 3) − k ²/
k 3
(m₂x²+k₂+k₂) (m₂x²+k₂+k₂) −R}
k ²
(m₂s² + k ₂+k₂)
(m₂x²+k₂ +k₂) (m₂x²+k₂+A₂)-R²
3)
k3
ooooo
F₂

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