A dynamic system is modeled as [4 ddot{x}+4 dot{x}+5 x=10 sin left(frac{1}{2} t ight), quad x(0)=frac{1}{2}, quad

A dynamic system is modeled as

\[4 \ddot{x}+4 \dot{x}+5 x=10 \sin \left(\frac{1}{2} t\right), \quad x(0)=\frac{1}{2}, \quad \dot{x}(0)=0\]

Plot the response \(x(t)\) for \(0 \leq t \leq 20\) by

a. Using the lsim command.

b. Simulating the Simulink model.