Analysis of Engineering Systems $-$ MAE $488$

Homework # $1$

Instructions: SHOW YOUR WORK! If insufficient work is shown, you will receive no credit $($even for a correct answer$).$ All handwritten portions of the homework MUST be on standard green engineering paper $($available at the bookstore, Staples, Amazon, etc.$)$ If you need some for the first assignment, just let me know. Every problem must have a handwritten portion with: problem number, a brief problem statement, what is given, and the solution $($may only be a statement to "see Matlab"$).$ See the Homework Requirements document which includes an example homework!! Note that although the code is provided in the example homework, it is not required.

As always, be sure to include units where appropriate. All plots should have labels on each axis $($with units$),$ a title $($e$.$g$.$ "MAE $488,$ Homework $1,$ Problem $1,$ Part a$"),$ and a legend if more than one plot is in the same figure $($except for subplots$).$

It may have been a while since you used MATLAB so I expect that you may have questions. I strongly suggest that you make use of the resources for this class especially the TA's and me if you have any questions. However, before doing so$,$ please make use of the "help" command in MATLAB $($e$.$g help plot$)$

$(9$ points$)$ The mass of a wheel is $10$ slugs.

a$.$ Calculate the mass in SI units.

b$.$ Calculate the weight in FPS units.

c$.$ Calculate the weight in SI units.

$(31$ points$)$ The displacement of a wheel is given by $y(t)=$Asin$(Bt+)$ where $t$ is time in seconds, $A=2in.,B=4ra\frac{d}{s},$ and $=0\mathrm{.}75$rad.

a$.(3$ points$)$ What is the amplitude?

b$.(3$ points$)$ What is the radian frequency?

c$.(3$ points$)$ What is the cyclic frequency in $Hz?$

d$.(3$ points$)$ What is the period?

e$.(3$ points$)$ What is the phase?

f$.(3$ points$)$ What is the equation for the velocity?

g$.(3$ points$)$ What is the equation for the acceleration?

h$.(10$ points$)$ Plot the displacement, velocity, and acceleration for $2$ seconds $($timestep of $0\mathrm{.}001$ seconds$)$ in a single figure with each plot in a subplot $($displacement at the top, acceleration at the bottom$).$ Include axis labels and title the plot "MAE $488,$ Homework $1,$ Problem $2,$ Part h$".$ Use a solid blue line for displacement, a dash$-$dot red line for velocity, and a dashed green line for acceleration. $($hint: use the MATLAB commands figure, subplot, plot, xlabel, ylabel, and title$).$ See the example on the next page.