Menu Close

1-Montrer-par-recurrence-que-la-transformee-deLaplace-suivante-L-f-n-t-p-p-n-L-f-t-p-p-n-1-f-0-p-n-2-f-0-f-n-1-0-2-Calaculer-partir-de-L-sint-p-la-transforme-L-

Tinku Tara 0 Comments
Pin




Question Number 143481 by lapache last updated on 15/Jun/21
1−Montrer par recurrence que la transformee deLaplace suivante L(f^n (t))(p)=p^n L(f(t)(p)−p^(n−1) f(0^+ )−p^(n−2) f ′(0^+ )−.......−f^((n−1)) (0^+ ) 2−Calaculer partir de L(sint)(p) la transforme L(((sint)/t))(p)
1−MontrerparrecurrencequelatransformeedeLaplacesuivanteL(fn(t))(p)=pnL(f(t)(p)−pn−1f(0+)−pn−2f′(0+)−…….−f(n−1)(0+)2−CalaculerpartirdeL(sint)(p)latransformeL(sintt)(p)
Commented by Ar Brandon last updated on 15/Jun/21
Non non. Nous n′allons pas montrer cela. 😝
Nonnon.Nousn′allonspasmontrercela.😝
Commented by lapache last updated on 15/Jun/21
Alors que c′est meme ce que je veux
Alorsquec′estmemecequejeveux
Commented by Ar Brandon last updated on 15/Jun/21
Mais c_ξ a a e^� te^� fait. Juste en bas.
Maisext\cccaaet´e´fait.Justeenbas.
Answered by Ar Brandon last updated on 15/Jun/21
L(sint)p=∫_0 ^∞ sin(t)e^(−pt) dt =[(e^(−pt) /(p^2 +1))(−psint−cost)]_0 ^∞ =(1/(p^2 +1)) L(((sint)/t))p=∫_0 ^∞ ((sint)/t)e^(−pt) dt L ′(((sint)/t))p=−∫_0 ^∞ sin(t)e^(−pt) dt=−(1/(p^2 +1)) L(((sint)/t))p=−arctan(p)+C lim_(p→∞) L(((sint)/t))p=−(π/2)+C=0⇒C=(π/2) L(((sint)/t))p=(π/2)−arctan(p)
L(sint)p=∫0∞sin(t)e−ptdt=[e−ptp2+1(−psint−cost)]0∞=1p2+1L(sintt)p=∫0∞sintte−ptdtL′(sintt)p=−∫0∞sin(t)e−ptdt=−1p2+1L(sintt)p=−arctan(p)+Climp→∞L(sintt)p=−π2+C=0⇒C=π2L(sintt)p=π2−arctan(p)

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *