# A linear system is modeled as [frac{2}{5} dot{x}+3 x=frac{5}{3} u(t)+u_{r}(t), quad x(0)=0] where (u(t)) and (u_{r}(t)) denote

## Question:

A linear system is modeled as

\[\frac{2}{5} \dot{x}+3 x=\frac{5}{3} u(t)+u_{r}(t), \quad x(0)=0\]

where \(u(t)\) and \(u_{r}(t)\) denote the unit-step and unit-ramp functions, respectively.

**a.** Express the response \(x(t)\) in closed form.

**b.** \(\$\) Plot the response \(x(t)\) by using the lsim command.

## Step by Step Answer:

**Related Book For**

## Modeling And Analysis Of Dynamic Systems

**ISBN:** 9781138726420

3rd Edition

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