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A. Determine the solution of a one dimensional and damped linear oscillating system to a spike impulse. A spike impulse means that the interval of the impulse t→0 while the amplitude A→o but their product At is finite and a constant. Let the natural frequency of oscillation be w0 and the damping parameter is B.

A. Determine the solution of a one dimensional and damped linear oscillating system to a spike impulse. A spike impulse means that the interval of the impulse t→0 while the amplitude A→o but their product At is finite and a constant. Let the natural frequency of oscillation be w0 and the damping parameter is B.

Elements Of Electromagnetics
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. Determine the solution of a one dimensional and damped linear oscillating system to a spike impulse. A spike impulse means that the interval of the impulse t→0 while the amplitude A→o but their product At is finite and a constant. Let the natural frequency of oscillation be w0 and the damping parameter is ß. B. Now, any arbitrary function can be represented as a series of impulses, therefore construct the inhomogeneous part of the solution using a Green's function where the Green's function is basically solution to part A (multiplied with some constant). C. Using Green's function method, find the solution of the inhomogeneous part of x(t) for a driving force given as F(t) = A exp(-bt) operating between O and t.
Transcribed Image Text:A. Determine the solution of a one dimensional and damped linear oscillating system to a spike impulse. A spike impulse means that the interval of the impulse t→0 while the amplitude A→o but their product At is finite and a constant. Let the natural frequency of oscillation be w0 and the damping parameter is ß. B. Now, any arbitrary function can be represented as a series of impulses, therefore construct the inhomogeneous part of the solution using a Green's function where the Green's function is basically solution to part A (multiplied with some constant). C. Using Green's function method, find the solution of the inhomogeneous part of x(t) for a driving force given as F(t) = A exp(-bt) operating between O and t.
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