Cálculo C

Lista 11

Exercício 1   Achar a solução de:

$$\begin{align*}a)\;&\ddot{x}+x=0;\quad x(2)=0,\quad\dot{x}(2)=0\\ b)\;&\ddot{y}+... ...f)\;&\ddot{y}-3\dot{y}+2y=e^{-t};\quad y(1)=0,\quad \dot{y}(1)=0\\ \end{align*}$$

Exercício 2   Encontrar as transformadas inversas de

$$\begin{align*}1)\;g(s)=& \frac{1}{s^2(s^2+9)}\\ 2)\;g(s)=& \frac{1}{\sqrt{s}}\\... ...\;g(s)=&\frac{s+4}{s^2+4s+8}\\ 5)\;g(s)=&\frac{8}{s^3(s^2-s-2)}\\ \end{align*}$$

Exercício 3   Resolva os sistemas abaixo:

$$\begin{align*}&\dot{x}+x-y=0 & \dot{y}+x=t\\ &\dot{y}-x+y=2 & \dot{x}+4y=0\\ & x(0)=1\quad y(0)=2 &y(0)=1,\quad x(0)=-1 \end{align*}$$

$$\begin{align*}&\dot{z}+\dot{y}=\cos t & \ddot{w}-2y=2\\ &\ddot{y}-z={\text {\ s... ...1 &w(0)=2,\quad \dot{y}(0)=2\\ & y(0)=1\quad \dot{y}(0)=0 & y(0)=1 \end{align*}$$

$$\begin{align*}&\dot{x}+5x-12y=0 & \dot{x}-2y=3\\ &\dot{y}+2x-5y=0 & \dot{y}+y-x=-t^2\\ & x(0)=8\quad y(0)=3 &x(0)=0,\quad y(0)=-1\\ \end{align*}$$

$$\begin{align*}&\ddot{x}=2\dot{x}+5y+3 & \ddot{x}+y=0\\ &\dot{y}=-\dot{x}-2y & \... ...=0\quad \dot{x}(0)=0 &x(0)=0,\quad \dot{x}(0)=-2\\ &y(0)=1 &y(0)=0 \end{align*}$$