Math Problem Statement
Problem #1: a) (3 pts) Using Laplace transform solve for x(t) in problem B-2-23 in your textbook (System Dynamics, Ogata, 4th edition). Please show all the steps in your solution. b) (1 pt) Using the Initial Value Theorem (IVT) and Final Value Theorem (FVT), find the initial value and final value (xss) of x(t). Use Οn = 0.5 rad/s. Hint: πΌππ = limπ β β π π(π ) and πΉππ = limπ β 0 π π(π ) c) (1 pt) Using Matlab, for the frequency Οn = 0.5 rad/s, plot x(t). What is the IV and FV from the plot?
Solution
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Math Problem Analysis
Mathematical Concepts
Laplace Transform
Differential Equations
System Dynamics
Control Systems
Formulas
Laplace transform: L{f(t)} = β«ββΊβ f(t)e^(-st)dt
Second-order system: sΒ²X(s) + 2ΞΆΟβsX(s) + ΟβΒ²X(s) = U(s)
Initial Value Theorem (IVT): limβββ sX(s)
Final Value Theorem (FVT): limββ0 sX(s)
Theorems
Initial Value Theorem (IVT)
Final Value Theorem (FVT)
Suitable Grade Level
University (Engineering/Applied Mathematics)
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