Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Transcribed Image Text:**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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