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Консультация № 186211
27.05.2012, 11:41
78.80 руб.
27.05.2012, 14:20
0
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
на фото: Задача N6; Вариант N7
фото:
на фото: Задача N6; Вариант N7
фото:
Обсуждение
27.05.2012, 12:19
общий
это ответ
Здравствуйте, Artek9300!
Переходим к изображениям:
x''(t) -> p^2X(p)-px(0)-x'(0)=p^2X(p)-2
x'(t) -> pX(p)-x(0)=pX(p)
y''(t) -> p^2Y(p)-py(0)-y'(0)=p^2Y(p)-p
y'(t) -> pY(p)-y(0)=pY(p)-1
sht-sint-t -> 1/(p^2-1)-1/(p^2+1)-1/p^2
cht-cost -> p/(p^2-1)-p/(p^2+1)
p^2X(p)-2+pY(p)-1=1/(p^2-1)-1/(p^2+1)-1/p^2
p^2Y(p)-p+pX(p)=p/(p^2-1)-p/(p^2+1)
pX(p)+Y(p)=1/(p(p^2-1))-1/(p(p^2+1))-1/p^3+3/p
pY(p)+X(p)=1/(p^2-1)-1/(p^2+1)+1
Решение системы:
X(p)=1/(p^2-1)-1/(p^2+1)+1-p^2/(p^2+1)+1/p^2=1/p^2+1/(p^2-1)
Y(p)=2/(p(1-p^2))-1/(p(1+p^2))-1/(p^3(1-p^2))-p/(1-p^2)=p/(p^2+1)-1/p^3
Возвращаемся к оригиналам:
x(t)=t+sht
y(t)=cost-t^2/2
Переходим к изображениям:
x''(t) -> p^2X(p)-px(0)-x'(0)=p^2X(p)-2
x'(t) -> pX(p)-x(0)=pX(p)
y''(t) -> p^2Y(p)-py(0)-y'(0)=p^2Y(p)-p
y'(t) -> pY(p)-y(0)=pY(p)-1
sht-sint-t -> 1/(p^2-1)-1/(p^2+1)-1/p^2
cht-cost -> p/(p^2-1)-p/(p^2+1)
p^2X(p)-2+pY(p)-1=1/(p^2-1)-1/(p^2+1)-1/p^2
p^2Y(p)-p+pX(p)=p/(p^2-1)-p/(p^2+1)
pX(p)+Y(p)=1/(p(p^2-1))-1/(p(p^2+1))-1/p^3+3/p
pY(p)+X(p)=1/(p^2-1)-1/(p^2+1)+1
Решение системы:
X(p)=1/(p^2-1)-1/(p^2+1)+1-p^2/(p^2+1)+1/p^2=1/p^2+1/(p^2-1)
Y(p)=2/(p(1-p^2))-1/(p(1+p^2))-1/(p^3(1-p^2))-p/(1-p^2)=p/(p^2+1)-1/p^3
Возвращаемся к оригиналам:
x(t)=t+sht
y(t)=cost-t^2/2
Форма ответа
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