![2. Find the unit step response of: *(t) = -2 o=[,60 + [] .c) (t)- O y(t) = [2 3]x(t) by two methods (1): transfer function an](http://img.homeworklib.com/questions/2be86b30-6ab6-11eb-b496-5b80cb08c009.png?x-oss-process=image/resize,w_560)
I have the first method complete, but I can't figure out the second method Could someone please show how to use the second method?
2. Find the unit step response of:
$$ \begin{aligned} \dot{\overrightarrow{\mathbf{x}}}(t) &=\left[\begin{array}{cc} 0 & 1 \\ -2 & -2 \end{array}\right] \overrightarrow{\mathbf{x}}(t)+\left[\begin{array}{l} 1 \\ 1 \end{array}\right] u(t) \\ y(t) &=\left[\begin{array}{cc} 2 & 3 \end{array}\right] \overrightarrow{\mathbf{x}}(t) \end{aligned} $$
by two methods (1): transfer function and then (2) \(y(t)=\mathbf{C} e^{\mathbf{A} t} \overrightarrow{\mathbf{x}}(0)+\mathbf{C} \int_{0}^{t} e^{\mathbf{A}(t-\tau)} \mathbf{B} u(\tau) d \tau+\mathbf{D} u(t)\). Re-
member that the Laplace transform of the unit step is \(u(s)=\frac{1}{s}\).
Homework Answers
![Y(t) = s(4-2) 3.2lt?) ult-2) -(2) I lutede. s(t-1)-22 (+- 2 - [-st-2) ett ult-2) 4(e)] ult-t 3e - 9() - (2 de | 2 (2-t) - 2e](http://img.homeworklib.com/questions/5231af60-6ab6-11eb-bd08-2980c202c610.png?x-oss-process=image/resize,w_560)
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I have the first method complete, but I can't figure out thesecond method. I have...
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Let \(\left\{\varphi_{n}(x)\right\}\) be an orthogonal set of functions on \([a, b]\) such that \(\psi_{0}(x)=1\) and \(\varphi_{1}(x)=x\), Show that \(\int_{a}^{b}(\alpha x+\beta) \varphi_{n}(x) d x=0\) for \(n=2,3, \ldots\) and any constants \(\alpha\) and \(\beta\),First we note that \(\alpha x+\beta=(\square) \Phi_{1}(x)+(\square \quad) \Psi_{0}(x)\).Using this together with the fact that \(\varphi_{0}\) and \(\varphi_{1}\) are orthogonal to \(\varphi_{n}\) for \(n>1\), we have the following.$$ \begin{aligned} \int_{a}^{b}(\alpha x+\beta) \varphi_{n}(x) d x &=\int_{a}^{b} a x \psi_{n}(x) d x+\int_{a}^{b} \beta \varphi_{n}(x) d x \\ &=\int_{a}^{b}\left(\square_{0}\right) \varphi_{1}(x) \varphi_{n}(x) d...
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1. ( 8 points) An object moves though a vector field, \(\overrightarrow{\mathbf{F}}(x, y)\), along a circular path, \(\overrightarrow{\mathbf{r}}(t)\), starting at \(P\) and ending at \(Q\) as shown in the graph below.(a) At the point \(R\) draw and label a tangent vector in the direction of \(d \overrightarrow{\mathbf{r}}\).(b) At the point \(R\) draw and label a vector in the direction of the vector filed, \(\overrightarrow{\mathbf{F}}(R)\).(c) At the point \(R\) is \(\overrightarrow{\mathbf{F}} \cdot d \overrightarrow{\mathbf{r}}\) positive, negative, or zero? Circle the correct...
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