A linear system is one that satisfies the principle of superposition. In other words, if an input u₁yields the output y₁, and an input u2 yields the output y2, the system is said to be linear if a com-bination of the inputs u = u₁ + u2 yield the sum of the outputs y = y1 + y2.Using this fact, determine the output y(t) of the following linear system:given the input:P(s) ==Y(s)U(s)=s+1s+10u(t) = e−2+ sin(t)=e

Step 1: Step 2: Step 3: Step 4:

Answered: A linear system is one that satisfies…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
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