**Homework Problem 7.2.1****Task:** Derive the equations of motion of the three mass system shown in the figure. Determine the transfer function x(s)/F(s) for the system described. **Parameter Values:** - \( m_1 = 1 \)- \( m_2 = 1 \)- \( m_3 = 1 \)- \( c_1 = 3 \)- \( c_2 = 4 \)- \( k_1 = 5 \)- \( k_2 = 25 \)*Assumption: If (z > y > x).***Diagram Explanation:**The diagram depicts a mechanical system comprising three masses, \( m_1 \), \( m_2 \), and \( m_3 \), connected in series. The components are connected by springs and dampers as indicated by:- **For \( m_1 \):** Attached to a spring \( k_1 \) and a damper \( c_1 \).- **For \( m_2 \):** Connected to \( m_1 \) via \( k_1 \), also having a spring \( k_2 \) and a damper \( c_2 \) connecting to \( m_3 \).- **For \( m_3 \):** Connected to \( m_2 \) via \( k_2 \).The forces are applied as follows:- \( F \) is applied downward on \( m_3 \).- Displacements are indicated by \( x \), \( y \), and \( z \), corresponding to each mass respectively. Analyze the system to determine its transfer function, showing how the input force \( F \) affects the displacement \( x \).

Homework Problem 7.2.1 Derive the equations of motion of the three mass system shown in figure. Determine the transfer function x(s)/F(s) for the system shown. The parameter values are as follows: m1=1, m2=1, m3=1, cl=3 c2=4, kl=5,and k2-25. If (z>y>x). X Y Z K1 K2 m1 401 m2 m3 JC2

Homework Problem 7.2.1 Derive the equations of motion of the three mass system shown in figure. Determine the transfer function x(s)/F(s) for the system shown. The parameter values are as follows: m1=1, m2=1, m3=1, cl=3 c2=4, kl=5,and k2-25. If (z>y>x). X Y Z K1 K2 m1 401 m2 m3 JC2

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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**Homework Problem 7.2.1**

**Task:** Derive the equations of motion of the three mass system shown in the figure. Determine the transfer function x(s)/F(s) for the system described.

**Parameter Values:**
- \( m_1 = 1 \)
- \( m_2 = 1 \)
- \( m_3 = 1 \)
- \( c_1 = 3 \)
- \( c_2 = 4 \)
- \( k_1 = 5 \)
- \( k_2 = 25 \)

*Assumption: If (z > y > x).*

**Diagram Explanation:**

The diagram depicts a mechanical system comprising three masses, \( m_1 \), \( m_2 \), and \( m_3 \), connected in series. The components are connected by springs and dampers as indicated by:

- **For \( m_1 \):** Attached to a spring \( k_1 \) and a damper \( c_1 \).
- **For \( m_2 \):** Connected to \( m_1 \) via \( k_1 \), also having a spring \( k_2 \) and a damper \( c_2 \) connecting to \( m_3 \).
- **For \( m_3 \):** Connected to \( m_2 \) via \( k_2 \).

The forces are applied as follows:
- \( F \) is applied downward on \( m_3 \).
- Displacements are indicated by \( x \), \( y \), and \( z \), corresponding to each mass respectively.

Analyze the system to determine its transfer function, showing how the input force \( F \) affects the displacement \( x \).

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