dx +2 + x = F(t), dt A (non-dimensional) driven-damped harmonic oscillator model results in the following ordinary dif- ferential equation for the amplitude function x(t): d²x dt² where F(t) represents the action of the driving force. **** (ii) Solve (x) in Fourier space in terms of (w). (iii) Write the solution for x(t) in physical space as a convolution. 810 60000 (i) Take the Fourier transform of (x) to show what is the relation between (w) and (w), being them the Fourier transforms of x(t) and F(t), respectively. (iv) Find the solution ä(t) for t > 1 assuming that F(t) = { 0: 5 : 0
dx +2 + x = F(t), dt A (non-dimensional) driven-damped harmonic oscillator model results in the following ordinary dif- ferential equation for the amplitude function x(t): d²x dt² where F(t) represents the action of the driving force. **** (ii) Solve (x) in Fourier space in terms of (w). (iii) Write the solution for x(t) in physical space as a convolution. 810 60000 (i) Take the Fourier transform of (x) to show what is the relation between (w) and (w), being them the Fourier transforms of x(t) and F(t), respectively. (iv) Find the solution ä(t) for t > 1 assuming that F(t) = { 0: 5 : 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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Transcribed Image Text:dx
+2 + x = F(t),
dt
A (non-dimensional) driven-damped harmonic oscillator model results in the following ordinary dif-
ferential equation for the amplitude function x(t):
d²x
dt²
where F(t) represents the action of the driving force.
****
(ii) Solve (x) in Fourier space in terms of (w).
(iii) Write the solution for x(t) in physical space as a convolution.
810
60000
(i) Take the Fourier transform of (x) to show what is the relation between (w) and (w), being
them the Fourier transforms of x(t) and F(t), respectively.
(iv) Find the solution ä(t) for t > 1 assuming that F(t) = { 0:
5 : 0<t<1
otherwise
(*)
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