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Consider the continuous-time LTI system 2y"(t)-5y' (t)-7 y(t) = -3x"(t) + 11x(t) (a) Find the transfer function for the system analytically. |

Consider the continuous-time LTI system 2y"(t)-5y' (t)-7 y(t) = -3x"(t) + 11x(t) (a) Find the transfer function for the system analytically. |

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Hello. I am getting hung up on this transfer function. I must not be calculating omega right.

Could you help me with this problem? Thank you for your time. 

**Title: Analysis of a Continuous-Time LTI System** **Introduction:** In this educational page, we will explore the process of finding the transfer function for a given continuous-time Linear Time-Invariant (LTI) system. **Problem Statement:** Consider the continuous-time LTI system described by the following differential equation: \[ 2y''(t) - 5y'(t) - 7y(t) = -3x''(t) + 11x(t) \] **Task:** (a) Find the transfer function for the system analytically. **Explanation:** The given differential equation relates the input \( x(t) \) and the output \( y(t) \). To find the transfer function, we utilize the Laplace Transform, which transforms differential equations into algebraic equations in the Laplace domain. The transfer function is the ratio of the Laplace Transform of the output \( Y(s) \) to the Laplace Transform of the input \( X(s) \). **Conclusion:** By completing this exercise, students will gain an understanding of how to analyze continuous-time LTI systems and derive their transfer functions analytically.
Transcribed Image Text:**Title: Analysis of a Continuous-Time LTI System** **Introduction:** In this educational page, we will explore the process of finding the transfer function for a given continuous-time Linear Time-Invariant (LTI) system. **Problem Statement:** Consider the continuous-time LTI system described by the following differential equation: \[ 2y''(t) - 5y'(t) - 7y(t) = -3x''(t) + 11x(t) \] **Task:** (a) Find the transfer function for the system analytically. **Explanation:** The given differential equation relates the input \( x(t) \) and the output \( y(t) \). To find the transfer function, we utilize the Laplace Transform, which transforms differential equations into algebraic equations in the Laplace domain. The transfer function is the ratio of the Laplace Transform of the output \( Y(s) \) to the Laplace Transform of the input \( X(s) \). **Conclusion:** By completing this exercise, students will gain an understanding of how to analyze continuous-time LTI systems and derive their transfer functions analytically.
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