Be sure to label and title all plots.
1). For the following differential equation: (d^2y/dt^2)+(2dy/dt)+(8y)=(-2dx/dt)+(8x)
a. Develop the simulation using integrators and run that simulation for x being a unit step. Plot y as a function of t.
b. Replace the analog integrator with a forward Euler integrator and trapezoidal integrator using a sampling time of 0.05. Run both the Euler and trapezoidal simulations and plot the output y.
c. For the trapezoidal integrator, there is an algebraic loop. Eliminate that loop by developing the difference equation for y(n) analytically again for a sampling time of 0.05. Hint for the trapezoidal integrator, the discrete-time transfer function is given
d. Write a Matlab® script to solve the difference equation.
e. Compare results to analog, the forward Euler, the trapezoidal simulation, and the result by solving and eliminating the algebraic loop in part c.
