# A Consider [begin{cases}dot{x}_{1}=-x_{1}left|x_{1} ight|+a x_{2}-frac{2}{3}+sin t & x_{1}(0)=frac{2}{3} dot{x}_{2}=-x_{1}-frac{1}{2} x_{2}-1, & x_{2}(0)=1end{cases}] where (a) is a

## Question:

A Consider

\[\begin{cases}\dot{x}_{1}=-x_{1}\left|x_{1}\right|+a x_{2}-\frac{2}{3}+\sin t & x_{1}(0)=\frac{2}{3} \\ \dot{x}_{2}=-x_{1}-\frac{1}{2} x_{2}-1, & x_{2}(0)=1\end{cases}\]

where \(a\) is a parameter. Using the RK4 method, plot \(x_{1}\) versus \(0 \leq t \leq 10\) for the two cases \(a=1.25\) and \(a=2.5\) in the same graph.

## Step by Step Answer:

**Related Book For**

## Modeling And Analysis Of Dynamic Systems

**ISBN:** 9781138726420

3rd Edition

**Authors:** Ramin S. Esfandiari, Bei Lu