Spring 2025

EXAM 2

ME 635 Modeling and Simulation

Answer all the questions. You can use any of the Simulink Models and Arena examples from the

class, and your HW submission for solving the questions. Use ChatGPT, Copilot etc. at your own

risk as the codes produced can be incorrect. Please include a GenAI statement in your submission

if you utilize any of the GenAI tools.

IMPORTANT NOTES:

• The answers and solutions to your problems should be typed out or written in one single

document and submitted as a single PDF document.

• MATLAB/Simulink, Arena are the only two applications needed for this exam. The

respective files for each application must be submitted along with your main submission

file. Formatting and the file submissions are valued at 10 points. Improper formatting will

cost point penalties.

• The problems are labelled by hand/analytical, MATLAB/Simulink, and Arena, indicating

the expected way of solving the problem.

• Strictly no credit after the due date/time for the Exam submission.

• Please give yourself at least 15 minutes to upload the files.

• Check your submission for readability and make sure there are no issues once

uploaded

• Plagiarism: 90% penalty to all copies, if the answer is correct.

1. [By hand – 10 points] For the system shown below in Figure 1:

a. Draw the free body diagrams for masses M and M . Write the modeling equations

1 2

describing the system. Consider the effect of gravity on these masses.

b. Write the state variable equations for the system (in Figure 1)

Figure 1: Mass Spring Damper System for Problem 1

2. [MATLAB and by hand – 25 points] For the system shown in Figure 2, the displacements

x and x are measured relative to M . Both springs are undeflected when x =x =0.

1 2 3 1 2

a. Write the equations of motion and draw the FBDs for each mass.

b. Develop a dynamic model in Simulink and run it for 200 seconds for the following

inputs:

M1 = M2 = 3 kg; and M3 = 5 kg

K = K = 125 N/m; B =B = 15 N.s/m;

1 2 1 2

F(t) = 100*[H(t - 1) - H(t - 10)] N *H is the Heaviside step function

c. Plot the displacement and velocity plots for each of the three masses in MATLAB,

by exporting the Simulink output to MATLAB workspace. Show necessary

plots in the main submission file along with your input forcing function.

Figure 2: Mass Spring Damper System for Problem 2

3. [Arena – 20 points] An office assigns customers to three lines based on their residence for

license plate processing. Each line has an exponential interarrival distribution with a mean

of 10 minutes, starting at time 0. Each customer type has a dedicated clerk with a service

time of UNIF (8, 10) minutes. Afterward, all customers go to a single clerk for form checks

and plate issuance with a service time of UNIF (2.65, 3.33) minutes. Run this model for

5,000 minutes to observe average and maximum system times.

Further, a consultant suggested using one line with three clerks processing any customer

type. Develop this model, run it for 5,000 minutes, and compare the results with the first

system. Include text boxes in your Arena files with the numerical results.

4. [Arena – 35 points] A part is introduced into the system every 10 minutes, beginning at

time zero. The system comprises three workstations (A, B, and C), each equipped with a

single machine. There are four types of parts, each having an equal likelihood of being

processed. The processing plans for these four-part types are detailed below, with process

times expressed as parameters for a triangular distribution (in minutes).

Workstation/Process Workstation/Process Workstation/Process

Part

Time Time Time

Part 1 A (5,8.5,11.5) C (8,13.1,18.5) -

Part 2 A (8.9,13.5, 18.1) B (7,14,21) C (4.2,8.2, 12.5)

Part 3 A (8.3, 11.6, 15.5) B (5.3,9.5,13.7) -

Part 4 B (9.2, 12.4, 16) C (8.5, 11.4,14) -

Assume that the transfer time between arrival and the first station, between all stations,

and between the last station and the system exit is 3 minutes. Use the Sequence feature

to direct the parts through the system and assign the processing times at each station.

Utilize the Sets feature to collect cycle times (total times in system) for each of the part

types independently. Animate your model (including part transfers), run the simulation

for a single replication of 10,000 minutes, and collect statistics on the average part cycle

time (report this in a text box in your Arena model file).

How many replications would you suggest running to increase confidence in the

developed model?