1. For the system shown below: 2 1 R, R2 es C (a) write the state equations of motion for the system using energy storage vari- ables as state variables. (b) draw a block diagram representation of the system and reduce the block dia- gram to find the transfer function T(s) = between the input e,(t) and the output e2g(t), and E,(s) (c) identify the effective mass, damping and stiffness of the second order system. 3.
1. For the system shown below: 2 1 R, R2 es C (a) write the state equations of motion for the system using energy storage vari- ables as state variables. (b) draw a block diagram representation of the system and reduce the block dia- gram to find the transfer function T(s) = between the input e,(t) and the output e2g(t), and E,(s) (c) identify the effective mass, damping and stiffness of the second order system. 3.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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1. **Circuit Explanation:**
The circuit consists of:
- A voltage source \( e_s \).
- Two resistors \( R_1 \) and \( R_2 \).
- A capacitor \( C \).
- An inductor \( L \).
The currents \( i_1 \), \( i_2 \), and \( i_3 \) flow through the respective components, with the circuit being grounded at point \( g \).
2. **Tasks:**
(a) Write the state equations of motion for the system using energy storage variables as state variables.
(b) Draw a block diagram representation of the system and reduce the block diagram to find the transfer function \( T(s) = \frac{E_{2g}(s)}{E_s(s)} \) between the input \( e_s(t) \) and the output \( e_{2g}(t) \).
(c) Identify the effective mass, damping, and stiffness of the second-order system.
**Graph/Diagram Explanation:**
- **Resistors** \( R_1 \) and \( R_2 \): Linear elements that offer resistance to the flow of current.
- **Capacitor** \( C \): Stores energy in an electric field.
- **Inductor** \( L \): Stores energy in a magnetic field.
- **Voltage Source** \( e_s \): Provides electrical energy.
This system illustrates the interaction of resistive, capacitive, and inductive components, forming a foundation for analyzing electrical networks and identifying system dynamics through state equations and transfer functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6dd7a041-f318-4736-992d-437cde8f3ed3%2F028030ea-c302-4d18-8d2e-3e6160194f42%2Frvkc60og_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem - Electrical Circuit Analysis
**Problem Statement:**
For the system shown below:
1. **Circuit Explanation:**
The circuit consists of:
- A voltage source \( e_s \).
- Two resistors \( R_1 \) and \( R_2 \).
- A capacitor \( C \).
- An inductor \( L \).
The currents \( i_1 \), \( i_2 \), and \( i_3 \) flow through the respective components, with the circuit being grounded at point \( g \).
2. **Tasks:**
(a) Write the state equations of motion for the system using energy storage variables as state variables.
(b) Draw a block diagram representation of the system and reduce the block diagram to find the transfer function \( T(s) = \frac{E_{2g}(s)}{E_s(s)} \) between the input \( e_s(t) \) and the output \( e_{2g}(t) \).
(c) Identify the effective mass, damping, and stiffness of the second-order system.
**Graph/Diagram Explanation:**
- **Resistors** \( R_1 \) and \( R_2 \): Linear elements that offer resistance to the flow of current.
- **Capacitor** \( C \): Stores energy in an electric field.
- **Inductor** \( L \): Stores energy in a magnetic field.
- **Voltage Source** \( e_s \): Provides electrical energy.
This system illustrates the interaction of resistive, capacitive, and inductive components, forming a foundation for analyzing electrical networks and identifying system dynamics through state equations and transfer functions.
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