Implement the following ODE in Simulink using a fixed step integration with a fixed step solver step of 0.1 seconds and use a unit step occurring at one second as the input.

+ + =

a) Create a MATLAB script to vary the value of zeta from 0.1 to 1.1 in increments of 0.1, capture the data in MATLAB, and plot the outputs on one graph for a 10 second simulation. b) Remove the unit step input and create an input back at MATLAB for the Simulink model where the control is 1 for the first 10 seconds and is -1 for the second 10 seconds (total sim time of 20 seconds). Set zeta to 0.5, use MATLAB to call the Simulink simulation, feeding the new control input to the simulation, and plot the results back at MATLAB