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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 (*)
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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