You are designing a read$/$write disk drive system as shown in Figure $1.$ The Equations

of Motion for the system can be written as:

$!!+$&$!")+(!")=$# $+$$

$""+$&$"!)+("!)=0$

Figure $1$: Read$/$Write disk drive

Create a Simulink simulation model of the system, assuming I $1=0\mathrm{.}77,$ I $2=0\mathrm{.}53,$

b $=0\mathrm{.}23,$ and k $=4\mathrm{.}37($units omitted for simplicity$).$ M D is a random number with a

mean of $0,$ a variance of $0\mathrm{.}001,$ a seed of $0,$ and a sample time of $0\mathrm{.}1$ seconds. Make

sure to add a scope to $\backslash$theta $1$ and $\backslash$theta $2$ in your Simulink model. Save the scope figure to an

image file $($e$.$g$.$ jpg$)$ and include with your submission.

a$)$ If M c is a sine input with an amplitude of $0\mathrm{.}5$ and a frequency of $1$ rad$/$s$,$ how long

does it take the read head to rotate $5$ radians $($round up to the nearest

$0\mathrm{.}1$ sec$)?$

t $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$)$ If M c is an impulse that lasts for $1$ second, has an amplitude of $0\mathrm{.}5,$ and begins at $2$

seconds, what is the steady$-$state rotational velocity for the read head?