Dynamics and Vibrations

Problem Sets

2022 Assignments

Matlab Assignment

Live Script Solution M File Solution
Due Date: Friday Feb 11, 2022
Suggested Schedule:
- Jan 26-Feb 1: Watch video tutorial
- Feb 2/Feb 7 Tutorial groups work on matlab
- Feb 3-Feb 10 Complete assignment
Video Tutorial (covers what you need for the problem set)
Matlab Tutorial (detailed written version)

Particle Motion
- Solutions MATLAB solutions Live script solution
- Due Date: Fri Feb 18, 2022
- Suggested Schedule:
  - Feb 3-Feb 8: Watch Episodes 2 and 3 of lecture videos
  - Feb 9/14 Tutorial groups work on particle kinematics
  - Feb 11-17 Complete assignment
- Video Help>> Prob 1> Prob 2> Prob 3> Prob 4> Prob 5> Prob 6> Prob 7>
- Data file for problem 2
- Data description for problem 2
Particle Dynamics
- Solutions MATLAB solutions
- Due Date: Fri Feb 25, 2022
- Suggested Schedule:
  - Feb 10-15 watch Episodes 4 and 5 of lecture videos
  - Feb 16/23 Tutorial groups work on particle dynamics
  - Feb 18-24 Complete assignment
- Video Help>> Prob 1> Prob 2> Prob 3> Prob 4> Prob 5>
- animate_planets.m
Energy/Momentum/Collisions for particles
- Solutions
- Due Date: Fri March 11 2022
- Suggested Schedule:
  - Feb 17-March 3 watch Episodes 6-9 of lecture videos
  - Feb 28/March 2 and March 7/9: Tutorial groups work on energy/momentum
  - March 4-10 Complete assignment
- Video Help>> Prob 1> Prob 2> Prob 3> Prob 4> Prob 5> Prob 6>
- digitize_image.m (code to extract x-y coords of points on an image)
- Frog_jump.gif
- Frog_jump.jpg
Free Vibrations

Solutions
Due Date: Fri March 25 2022
Suggested Schedule:
- March 10-17: Watch Episodes 11-13 of lecture videos
- March 21/23: Tutorial groups work on free vibrations
- March 18-24 Complete assignment
Video Help:>> Prob 1> Prob 2> Prob 3> Prob 4> Prob 5> Prob 6> Prob 7>

Forced Vibrations

Solutions
Due Date: Fri April 8 2022
Suggested Schedule:
- March 22/24 Watch Episodes 14/15 of lecture videos
- April 4/6 Tutorial groups work on forced vibrations
- March 25-April 7 Complete assignment
Video Help>> Prob 1> Prob 2> Prob 3> Prob 4> Prob 5>

Rigid body kinematics / inertial properties

Solutions
Due Date: Fri April 22 2022
Suggested Schedule:
- April 5-14 Watch Episodes 16-18 of lecture videos
- April 18/20 Tutorial groups work on rigid body kinematics
- April 15-21 Complete assignment
Video Help>> Prob 1> Prob 2> Prob 3> Prob 4> Prob 5> Prob 6> Prob 7> Prob 8>

Rigid body dynamics

Solutions
Due Date: Fri April 29 2022
Suggested Schedule:
- April 19-21 Watch Episodes 19/20 of lecture videos
- April 25/27 Tutorial groups work on rigid body dynamics
- April 22-29 Complete assignment
Video Help>> Prob 1> Prob 2> (video demo) Prob 3> Prob 4> Prob 5>

General Homework Policies:

Homework is due by 5pm on the due date. If you forget to upload a homework and it's a few hours late that's usually not a problem; just upload it anyway. As long as a homework is submitted before graders have completed their work for the week, we will grade it. But we try hard not to inconvenience graders by sending them late submissions (graders are usually juggling multiple commitments, like all Brown students), so we only guarantee to grade work that is submitted by the 5pm deadline.
Submitting Homework: Please scan (or type) your homework solutions, save them in pdf format, and upload the pdf file to CANVAS.
Check that electronic submissions uploaded correctly - people often submit the wrong file by mistake. If this is discovered too late there is generally nothing we can do about it.

We will not count your lowest homework grade when computing your final grades. This is meant as an automatic homework excuse for sickness or an emergency. You don't need to request extensions on homework - we will just tell you to use the automatic excuse.
Collaboration policy: You may work on homework problems as a group. However, any work submitted for grading must represent work done by the person who will receive credit for the assignment. It is not acceptable for two students to submit identical copies of a homework problem. It is not acceptable for one student to copy work previously done by another.
Regrade requests: Please fill out the regrade request form (please submit a separate form for each assignment you need regrading). Homeworks will not be re-graded, but we will look at the assignment if you are close enough to a grade borderline at the end of the semester for the change in points to make any difference.
Deadline extensions: We will not extend HW deadlines other than through the flexibility offered by the normal grading policy. If you are taking the class for a grade, you can drop one homework. If you take the class S/NC you can submit up to 3 homeworks up to a week late, or if you prefer, skip 3 homeworks altogether and take the final instead.

Presenting your homework When you write your homework solutions a few simple steps will help optimize your grade. You can see a sample page of a well organized homework (from a fluids class, not ENGN40) here.
- Make sure your solutions to the problems are in the correct order.
- Identify each problem clearly
- If you skipped a problem, or part of a problem, write a note to the grader to let them know
- Show your work. It is not necessary to show every line of complicated algebra, but include enough detail to make sure the grader will know whether errors (if any!) are caused by just an algebra slip or a conceptual error. This is especially important for questions that ask you to 'show' some result.
- Make sure the grader can find the end result of your calculation.

IMPORTANT: We make up our own homework problems instead of taking them from a book, to make the course more up to date and relevant. One regrettable consequence of this policy is that the homework assignments will almost certainly contain mistakes. If you find something in an assignment that doesn't work out, check with a TA or faculty member to see if there is an error before spending hours looking for your own error.

2021 Assignments (ENGN40 was offered during summer semester in 2021 with an unusual schedule)

Matlab Assignment
- Solutions: Probs 1-6 Probs 7-11 (Right click and Save As...). If you download more than once a (1) will be inserted at the end of the filename. You will have to rename the file to remove this before you can open it with MATLAB.
- Image file for problem #9 (right click the link and select 'Save As...')
- Matlab Tutorial (detailed written version)
- Matlab Tutorial Video (covers what you need for the problem set)
Particle Kinematics
- Solutions (pdf) Matlab code Live Script
- Data files for prob 3: Figure-eight-fixed.csv Figure-eight-with-turn.csv
- Video demo for problem 3 (quadcopter flight)>
- Video Help>> Prob 1> Prob 2> Prob 3> Prob 4> Prob 5> Prob 6>
Particle Dynamics

Solutions (pdf): Live Script Matlab Code
Video Help>> Prob1> Prob2> Prob3> Prob4> Prob5> Prob6>

Energy and Momentum

Vibrations WARNING: This is a long homework (but you have 2 weeks to complete it)!

Solutions (pdf)
Video Help>> Prob1> Prob2> Prob3> Prob4> Prob5> Prob6> Prob7> Prob8> Prob9> Prob10>

Rigid Body Kinematics/Inertial Properties

Rigid Body Dynamics
- Solutions (pdf) >>
- Due Date: Friday August 6
- Video Help>> Prob1> Prob2> Prob3> Prob4> Prob5> Prob6>

2020 Assignments

Matlab Assignment (topics from MATLAB tutorial) Live Script Solutions MATLAB solutions
Image files for problem #10 (right click the link and select 'Save As...' cover_image.jpg payload_image.jpg
Particle Motion Data files for prob 2: Circle_fixedorientation.csv Circle_with_turn.csv Solutions MATLAB code
Particle Motion II Solutions MATLAB code
Energy and Momentum csv file for problem 5 Solutions
Vibrations I Solutions
Vibrations II Solutions Live Script
Rigid bodies I Solutions
Rigid bodies II Solutions

2019 Assignments

2018 Assignments

2017 Assignments

MATLAB assignment Due Friday February 3 2017. Mupad solutions LiveScript Solutions MATLAB solutions
Kinematics and Dynamics of Particles. Data file for problem 2 Due Friday Feb 10 Solutions Matlab Code
Calculating motion of particles with MATLAB Due Friday Feb 17 Solutions Matlab Code Mupad Code
Energy and Momentum. baseball movie track baseball code. Code to check prob 6 Solutions Matlab soln Mupad soln
Free Vibrations Solutions
Forced Vibrations Solutions
Rigid Bodies 1 animate_rotation.m Solutions
Rigid Bodies 2 Solutions

2016 Assignments

2015 Assignments

2014 Assignments

MATLAB assignment Solutions (mupad) Solutions (Matlab)
Kinematics and dynamics of particles (Due Fri Feb 7) Web page for bow and arrow experiments Solutions Matlab
Solving particle motion problems with MATLAB/Mupad (Due Fri Feb 14) animate_helicopter.m animate_pendulum.m Solutions Matlab code for solutions
Energy methods, Impulse and Momentum (Due Fri Feb 28). Solutions Note that we will cover impulse and momentum in class on Tues 25th.
Free (damped and undamped) vibrations Solutions (Due Fri March 21)
Forced vibrations (Solutions) (Due Fri April 4)
Rigid body kinematics Solutions
Rigid body dynamics data file for hydrofoil problem (csv file - can be read by matlab) (Solutions) (Due Fri April 25)

2013 Assignments

MATLAB assignment (Due Friday Feb 1). Mupad solutions Matlab solutions (Grading scheme is given in the HW). Before doing this assignment please work through sections 1-13 of the MATLAB tutorial, and then work through the Mupad tutorial. Brown users can download MATLAB from the CIS server.
Kinematics and dynamics of particles (Due Fri Feb 8) Solutions Additional optional un-graded practice problems (don't hand them in!) (From Nelson, et al, 'Engineering Mechanics: Dynamics Amazon link>>) Kinematics: 2.45, 2.48, 2.52, 2.58, 2.60, 2.66, 2.73, 2.75, .276 (hard) 2.81, 2.82, 2,86, 2.90, 2.98, 2.99, 2.104, 2.105, 2.106, Forces and motion: 3.32, 3.36, 3.37, 3.39, 3.43, 3.48, 3.49, 3.52, 5.68, 5.91, 5.92, 5.95, 5.96, 5.101, 5.106, 5.114, 5.123, 5.125, 5.140, 5.141, 5.155, Also for those who are still interested in Felix Baumgartner after wading through that tricky homework problem here's an article just published Feb 5 updating some of the statistics http://www.bbc.co.uk/news/science-environment-21341485
Solving equations of motion for particles. Solutions The matlab scripts to do the animations are here: animate_pendulum.m animate_quadrupole.m Additional optional un-graded practice problems (Nelson et al) 3.33, 3.45, 3.54 (the problem should read “show that the solution to the equation of motion is…”) 3.58, 3.59
Energy and Momentum for particles. Solutions Additional optional un-graded practice problems (Nelson et al) Work and Energy for particles 6.43, 6.44, 6.46, 6.47, 6.55, 6.57, 6.64, 6.66, 6.68, 6.79, 6.90. 6.92, 6.93, 6.94, 6.95 Impulse/Momentum for particles 7.54, 7.55, 7.59, 7.62, 7.84, 7.85, 7.86, 7.87, 7.89, 7.90, 7.97, 7.98, 7.100, 7.101, 7.102
Vibrations 1. Solutions Due Friday March 22 Optional ungraded practice problems: 8.3, 8.4,
8.5, 8.6, 8.7, 8.16, 8.18, 8.19, 8.20
Vibrations 2 Solutions Due Friday April 5
Rigid Bodies 1 Solutions Due Friday April 12
Rigid Bodies 2 Solutions Due Friday April 26

2012 Assignments

MATLAB assignment (Due Friday Feb 3). Solutions Before doing this assignment please work through sections 1-15 of the MATLAB tutorial. Brown users can download MATLAB from the CIS server. For off-campus use you will need to install the VPN client first, and make a VPN connection to Brown (the username and password for connecting to VPN are the same as those you use to access BANNER or your Brown email)
Kinematics and dynamics of Particles (Due Friday Feb 10). Solutions
Solving equations of motion for particles (Due Friday Feb 17) Solutions
Matlab scripts: animate_impeller.m animate_projectiles.m, animate_pendulum.m
Energy and Momentum for Particles (Due Friday March 2) Solutions
Free Vibrations (Due Friday March 23) Solutions
Forced Vibrations (Due Friday April 6) (Solutions) Correction
Rigid Bodies 1 (Due Friday April 13) Matlab file with helmet acceleration data Solutions MATLAB solution
Rigid Bodies 2 (Due Friday April 27) Solutions

2011 Assignments

MATLAB assignment (Due Friday Feb 4). Before doing this assignment please work through sections 1-15 of the MATLAB tutorial Solutions

Kinematics and dynamics of Particles (Due Friday Feb 11). Solutions

Solving equations of motion for particles (Due Friday Feb 18) Solutions

Energy and Momentum for Particles (Due Friday March 4) Solutions

Free Vibrations (Due Friday March 25) Solutions

Forced Vibrations (Due Friday April 8) Solutions

Rigid bodies Due Friday April 16 Solutions

Rigid bodies - due Friday April 29 Solutions. Note that there is a mistake in the solution for problem # 2, Eq. 4, which should read as a_x = - R theta_2_dot/2 instead of a_x = - R
theta_2_dot. However, the damage is contained. The only difference is, friction force is now f = (4/9) mg instead of mg/2. The disk still slips along the inclined plane and the rest of the solution is valid.

2010 Assignments

MATLAB assignment (Due Friday Feb 5). Before doing this assignment please work through sections 1-14 of the MATLAB tutorial Solutions
Particle Dynamics (Due Friday Feb 12) Solutions
Particle Dynamics 2 (Due Friday Feb 19) Solutions
Energy/Momentum (Due Friday March 5) MATLAB file for snooker problem Solutions
Vibrations 1 (Due Friday, March 26) Solutions
Vibrations 2 (Due Friday, April 9) Solutions - NOTE error in frequencies in final problem (Greenhouse Gas) of sqrt(3) that is not correct in solutions !!!
Rigid bodies 1 (Due Fri April 16)
Rigid bodies 2 solutions (Due Fri April 30)

2009 Assignments

MATLAB tutorial and MATLAB assignment (Due Friday Jan 30) Solutions
Particle dynamics (Due Friday Feb 6) Solutions
Analyzing motion of particles with MATLAB (Due Friday Feb 13) Solutions
Energy methods for particles (Due Friday Feb 27) Solutions
Linear and Angular Momentum for particles (Not graded - use as exam prep) Solutions
The matlab snooker simulation can be downloaded here
Vibrations 1 (Due Friday, March 20) Solutions NOTE: Prob. 2 depends on Lo. Assume L=Lo.
Vibrations 2 (Due Friday, April 3) (Last Problem revised slightly on March 29/30) Solutions
Vibs/Rigid-Body Project HW (Part 2 of the attached file, which is the Project description; new file with slight modifications to clarify analysis was posted 4/6/09) Solution
Kinematics of Rigid Bodies ; Solutions
Dynamics of Rigid Bodies ; Solutions