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.

\(\left\{\begin{array}{ll}2 \ddot{x}_{1}+2 x_{1}+3 \dot{x}_{1}-\frac{3}{2}\left(x_{2}-x_{1}\right)-4\left(\dot{x}_{2}-\dot{x}_{1}\right)=e^{-t / 4} \sin t, & x_{1}(0)=1, \dot{x}_{1}(0)=0 \\ \frac{3}{2}\left(x_{2}-x_{1}\right)+4\left(\dot{x}_{2}-\dot{x}_{1}\right)=e^{-t / 3} & x_{2}(0)=1\end{array}, 0 \leq t \leq 15\right.\)

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