1. A system has an input-output relationship represented by the following third order differential equation: y''(t) + 152y"(t) + 1700y'(t) + 2800y(t) = 1400f(t), where y(t) is the output and f(t) is the input. a. Provide an expression for the transfer function Y (s)/F(s). Assume the initial conditions are zero. b. Using the transfer function, if f (t) = 5.0 ustep (t), provide an equation for y(t). Assume the initial conditions are 0. Remember to multiply your answer by ustep (t). %3D Provide the state equations for the system with the state variables defined as: x1 (t) = y(t), x2(t) = y'(t) x3 (t) = y"(t) с. d. Provide the state equations for the system with the state variables defined as: x1 (t) = y"(t) x2 (t) = y'(t) x3 (t) = y(t)
1. A system has an input-output relationship represented by the following third order differential equation: y''(t) + 152y"(t) + 1700y'(t) + 2800y(t) = 1400f(t), where y(t) is the output and f(t) is the input. a. Provide an expression for the transfer function Y (s)/F(s). Assume the initial conditions are zero. b. Using the transfer function, if f (t) = 5.0 ustep (t), provide an equation for y(t). Assume the initial conditions are 0. Remember to multiply your answer by ustep (t). %3D Provide the state equations for the system with the state variables defined as: x1 (t) = y(t), x2(t) = y'(t) x3 (t) = y"(t) с. d. Provide the state equations for the system with the state variables defined as: x1 (t) = y"(t) x2 (t) = y'(t) x3 (t) = y(t)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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![**Differential Equations and Systems Analysis**
**Problem Statement:**
A system has an input-output relationship represented by the following third-order differential equation:
\[ y'''(t) + 152y''(t) + 1700y'(t) + 2800y(t) = 1400f(t), \]
where \( y(t) \) is the output and \( f(t) \) is the input.
**Tasks:**
a. Provide an expression for the transfer function \( \frac{Y(s)}{F(s)} \). Assume the initial conditions are zero.
b. Using the transfer function, if \( f(t) = 5.0 \, u_{step}(t) \), provide an equation for \( y(t) \). Assume the initial conditions are 0. Remember to multiply your answer by \( u_{step}(t) \).
c. Provide the state equations for the system with the state variables defined as:
- \( x_1(t) = y(t) \),
- \( x_2(t) = y'(t) \),
- \( x_3(t) = y''(t) \).
d. Provide the state equations for the system with the state variables defined as:
- \( x_1(t) = y''(t) \),
- \( x_2(t) = y'(t) \),
- \( x_3(t) = y(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11657d80-0b9a-4a9b-9635-8d2c2856a255%2Fd9b2f9bb-bcf7-4e30-888f-70b48e50789a%2Fx07bs5r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Differential Equations and Systems Analysis**
**Problem Statement:**
A system has an input-output relationship represented by the following third-order differential equation:
\[ y'''(t) + 152y''(t) + 1700y'(t) + 2800y(t) = 1400f(t), \]
where \( y(t) \) is the output and \( f(t) \) is the input.
**Tasks:**
a. Provide an expression for the transfer function \( \frac{Y(s)}{F(s)} \). Assume the initial conditions are zero.
b. Using the transfer function, if \( f(t) = 5.0 \, u_{step}(t) \), provide an equation for \( y(t) \). Assume the initial conditions are 0. Remember to multiply your answer by \( u_{step}(t) \).
c. Provide the state equations for the system with the state variables defined as:
- \( x_1(t) = y(t) \),
- \( x_2(t) = y'(t) \),
- \( x_3(t) = y''(t) \).
d. Provide the state equations for the system with the state variables defined as:
- \( x_1(t) = y''(t) \),
- \( x_2(t) = y'(t) \),
- \( x_3(t) = y(t) \).
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