Given the system information below with zero initial conditions, solve for x(t) using forward differencing method where u(t) = sin(t)
$H(s) = \frac{X(s)}{U(s)} = \frac{(s+4)}{s(s^2+5s+2)}$, t ? [0,20sec], dt = 0.01sec
• Derive the iterative equation using FD
• Develop a complete Matlab script that solves for x(t) and plot it against time.
Include all the labels and units.