Let the following equation d ^ 2y / dt ^ 2 + 0.5cos (y) dy / dt + sin (y) = 0 with y (0) = π / 2 and y '(0) = 1/2 (i) using π the runge-kutta method with u step Δt = 0.001π, solve the equation for tϵ [0; 4π] with a step of 0.5π unit. (ii) give the graphical representation of y (t) for tϵ [0; 4π]. (iii) give the graphical representation of y '(t) as a function of
Let the following equation d ^ 2y / dt ^ 2 + 0.5cos (y) dy / dt + sin (y) = 0 with y (0) = π / 2 and y '(0) = 1/2 (i) using π the runge-kutta method with u step Δt = 0.001π, solve the equation for tϵ [0; 4π] with a step of 0.5π unit. (ii) give the graphical representation of y (t) for tϵ [0; 4π]. (iii) give the graphical representation of y '(t) as a function of
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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Let the following equation d ^ 2y / dt ^ 2 + 0.5cos (y) dy / dt + sin (y) = 0
with y (0) = π / 2 and y '(0) = 1/2
(i) using π the runge-kutta method with u step Δt = 0.001π, solve the equation for tϵ [0; 4π] with a step of 0.5π unit.
(ii) give the graphical representation of y (t) for tϵ [0; 4π].
(iii) give the graphical representation of y '(t) as a function of y (t) for tϵ [0; 4π].
![Exercice 30 :
'La ciarté et la précision de la rédaction seront prises en compte dans l'appréciation de la copie.
Soit l'équation suivante
d²y
dy
dt-
+ 0.5cos(y)
+ sin(y) = 0,
dt
T
avec y(0) = " ei'(0) = ;
(i) En utilisant la méthode de Runge-Kutta avec un pas At = 0,001T, résoudre l'équation pour
%3D
te[0; 4 ] avec un pas de 0,5n unités.
(ii) Donner la représentation graphique de y(t) pour te[0; 4t ].
(iii) Donner la représentation graphique de y'(t) en fonction de y(t) pour te[0 ; 4x ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb86237c7-0ddc-4747-bf59-b2ad0e5b4dda%2F40ca50d6-4622-49c2-a18b-c38cdfa9cba8%2Fmz80ly_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercice 30 :
'La ciarté et la précision de la rédaction seront prises en compte dans l'appréciation de la copie.
Soit l'équation suivante
d²y
dy
dt-
+ 0.5cos(y)
+ sin(y) = 0,
dt
T
avec y(0) = " ei'(0) = ;
(i) En utilisant la méthode de Runge-Kutta avec un pas At = 0,001T, résoudre l'équation pour
%3D
te[0; 4 ] avec un pas de 0,5n unités.
(ii) Donner la représentation graphique de y(t) pour te[0; 4t ].
(iii) Donner la représentation graphique de y'(t) en fonction de y(t) pour te[0 ; 4x ]
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