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Consider a driven undamped spring/mass system described by the initial-value problem d²x + w²x = Fosin" yt, x(0) = 0, x'(0) = 0. di² (a) For n = 2, discuss why there is a single frequency Y₁/27 at which the system is in pure resonance. (b) For n = 3, discuss why there are two frequencies Y₁/27 and y2/27 at which the system is in pure resonance. (c) Suppose w = 1 and Fo= 1. Use a numerical solver to obtain the graph of the solution of the initial-value problem for n = 2 and y = y₁ in part (a). Obtain the graph of the solution of the initial-value problem for n = 3 corresponding, in turn, to y = y₁ and y = y2 in part (b).

Consider a driven undamped spring/mass system described by the initial-value problem d²x + w²x = Fosin" yt, x(0) = 0, x'(0) = 0. di² (a) For n = 2, discuss why there is a single frequency Y₁/27 at which the system is in pure resonance. (b) For n = 3, discuss why there are two frequencies Y₁/27 and y2/27 at which the system is in pure resonance. (c) Suppose w = 1 and Fo= 1. Use a numerical solver to obtain the graph of the solution of the initial-value problem for n = 2 and y = y₁ in part (a). Obtain the graph of the solution of the initial-value problem for n = 3 corresponding, in turn, to y = y₁ and y = y2 in part (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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Show this complete solution for this force driven without damping equation:

 

Consider a driven undamped spring/mass system described by the initial-value problem d²x + w²x = Fosin" yt, x(0) = 0, x'(0) = 0. di² (a) For n = 2, discuss why there is a single frequency Y₁/27 at which the system is in pure resonance. (b) For n = 3, discuss why there are two frequencies Y₁/27 and y2/2π at which the system is in pure resonance. (c) Suppose w = 1 and Fo= 1. Use a numerical solver to obtain the graph of the solution of the initial-value problem for n = 2 and y = y₁ in part (a). Obtain the graph of the solution of the initial-value problem for n = 3 corresponding, in turn, to y = y₁ and y = y2 in part (b).
Transcribed Image Text:Consider a driven undamped spring/mass system described by the initial-value problem d²x + w²x = Fosin" yt, x(0) = 0, x'(0) = 0. di² (a) For n = 2, discuss why there is a single frequency Y₁/27 at which the system is in pure resonance. (b) For n = 3, discuss why there are two frequencies Y₁/27 and y2/2π at which the system is in pure resonance. (c) Suppose w = 1 and Fo= 1. Use a numerical solver to obtain the graph of the solution of the initial-value problem for n = 2 and y = y₁ in part (a). Obtain the graph of the solution of the initial-value problem for n = 3 corresponding, in turn, to y = y₁ and y = y2 in part (b).
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