The governing equations and initial conditions of a dynamic system are provided. Plot the specified output(s), together with the input(s), by using the lsim command. Note that \(u(t)\) denotes the unit-step function.

\(\left\{\begin{array}{ll}\ddot{x}_{1}+\frac{5}{3} x_{1}-\frac{2}{3} x_{2}-3\left(\dot{x}_{2}-\dot{x}_{1}\right)=u(t) & x_{1}(0)=0, \dot{x}_{1}(0)=1 \\ \ddot{x}_{2}+\frac{2}{3}\left(x_{2}-x_{1}\right)+3\left(\dot{x}_{2}-\dot{x}_{1}\right)=\sin t^{\prime} & x_{2}(0)=1, \\ \dot{x}_{2}(0)=0^{\prime}\end{array} 0 \leq t \leq 20\right.\)

Outputs: \(x_{1}(t), x_{2}(t)\)