8A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically equal to times the instantaneous velocity. (Use g = 32 ft/s² for the accelerationdue to gravity.)Complete the Laplace transform of the differential equation.s²x{x} + ([])s£{x} +Use the Laplace transform to find the equation of motion x(t).x(t) =])L{x} = 0

Mass, m = 4-pound Length, l = 2 feet Height, h = 20-inches Damping force, df = 78 times…

-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the equilibrium position, and the resulting motion takes place in a medium offering a dampi to gravity.) nmplete the Laplace transform of the differential equation. 1)s. sx{x} + [ the Laplace transform to find the equation of motion x(e). ]+()*(x) = 0

-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the equilibrium position, and the resulting motion takes place in a medium offering a dampi to gravity.) nmplete the Laplace transform of the differential equation. 1)s. sx{x} + [ the Laplace transform to find the equation of motion x(e). ]+()*(x) = 0

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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laplace transform
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): 1. What is the order of this system?
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