Math Problem Statement

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The original query submitted by the user involves solving a control system problem, specifically using Laplace transforms and solving a differential equation for system response.

Solution

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Math Problem Analysis

Mathematical Concepts

Control Systems
Laplace Transform
System Dynamics

Formulas

G(s) = Kp / (Ts + 1)
ΔX(t) = L^{-1} { ΔX(s) G(s) }
Y(s) = 50 / s(s+1)
Y = 50C + C'e^{-50t}

Theorems

Laplace Transform Theorem
Inverse Laplace Transform
System Response Theorems

Suitable Grade Level

Undergraduate - Control Systems Engineering

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