$(20$ points$)$ Simulation. Use Simulink to create the model from $2$ b$.$ Simulate for $10$ seconds. Parameters

are $($Mass $=1000kg$; coefficient of air resistance $b=50N\frac{m}{s}$; Force of motor $=500N).$ Initial conditions

are $0.$

Post a screenshot of your model.

Export data to MATLAB and plot the velocity over $10$ seconds. Label the axes.

b$)(15$ points$)$ Create a model and block diagram to estimate a car's velocity. The forces acting upon

the car are the engine output $($simplified $-$ assume it's a force acting on the car$)$ and wind resistance

$(F=b$ bv where $b$ is a constant coefficient and $v$ is car velocity$).$ Output should be car velocity. Input is

car engine force. Assume a car is a mass.

Draw the free body diagram and derive the governing equation.

Create the block diagram for the equation calculated in $($b$\mathrm{.}1).$

c$)(10$ points$)$ Copy the block diagram from above and draw a dashed line box around the model

from $($b$)$ to identify it as your 'plant'. The plant represents the dynamics of your car given some input.

Your inputs and output will enter$/$exit this plant.

Add feedback control to regulate the car velocity $($cruise control$).$

Helpful notes.: $*$ Add a controller $/$ regulator block that provides input to your plant. We don't

know how to design the controller; use a block for the controller as a placeholder. $-$ What is the

output from a controller$/$regulator block? Hint: this is also the input to your plant $-$ what input is

the plant expecting? $*$ The input to the controller $/$ regulator is the error between actual speed and

desired speed.

a$)(15$ points$)$ A spring mass system with input force $($F$)$ and displacement

$($u$).$ Output is the position of mass $($z$).$ The governing equation is: $m{z}^{}=$

$F-kz+ku$

Rederive the governing equation $($i$.$e$.$ demonstrate that you can

also get this equation$).$ Show the FBD and write out the

equation of motion. Show your work!

Create the block diagram for the equation given in $($a$)$