Final Exam - solution and statistics

Click here for the posted SOLUTION for the final exam.

Click here for the final exam grade statistics.

Let me know if you have questions on the solution.

Vibrations in Electronics

Many modern electrical devices make use of microelectromechanical, or MEM, resonators and filters (pictured above) in their circuitry, especially those involving the wireless transmission of data such as cell phones and computers. One possible use for an MEM resonator would be to act as a bandpass filter, regulating the frequency output of a circuit (a possibility which has been researched by Purdue Mechanical Engineering professor Jeffrey Rhoads). The filter acts by having negligible motion until a signal is passed which results in the MEM device oscillating at resonance (approximately its natural frequency), at which point the vibrations of the structure reach a magnitude large enough for the wave to pass through. The following article discusses some recent breakthroughs in the area and the advantages of using MEM technology:

Article

Final Exam Answers?

Prof,
Will you be posting the answers to the final exam on here soon? I'm just curious on how to work a couple of the problems.
Thanks

Final exam question

Prof. Krousgrill,
For the 'kinetic' term in the work energy equation, can we choose two different points for the translational and rotational components of kinetic energy?
Thanks

Final Exam - some additional details

Thank you for your contributions for the short answer/short calculation questions on the exam. As stated earlier, there will be a total of 10 short answer/short calculation questions on the exam (five parts each on Problems 4 and 5). Note that 8 of these questions appearing on the exam are taken directly from your suggestions or were inspired by your suggestions. Good job.

Also, you will need to bring a straight edge for drawing on one of the questions.

The Tutorial Room will be open on Monday from 10AM to 1PM. I had planned to be in the room myself later in the afternoon. However, I have a retreat tomorrow afternoon that I need to attend elsewhere on campus.

I will ask Deb to schedule a room for our help session on Monday evening at 7PM. I will try to post this room here on the blog. However, if I am not able to do so, I will ask Deb to put up a note on my office door (ME 367) letting you know the location of the help session.

CMK

Can you write a good final exam question?

As detailed in the post below, Problems 4 and 5 on the final exam will have five parts each with each part being a short calculation/short answer question. Over the weekend, I wrote the final exam. However, I have come up empty in my search for a good fifth part of Problem No. 5.

I have decided to turn this part of Problem No. 5 over to the class. I am asking that you submit a short calculation/short answer question for the exam. Please attach your submission as a comment to this post (I cannot accept email submissions as the entire class needs to see these questions prior to the exam). You do not need to write out the problem in complete detail; providing ideas is acceptable. However, the more details that you provide on the question the better. Please submit only questions -- do not provide answers. More than one submission is fine. I need to have all questions by 10AM on Saturday, December 13.

I am committed to including one of your submissions for this problem provided that more than three questions are submitted. In fact, if more than one submission looks good, I will replace some of my questions with yours.

I look forward to seeing your questions.

CMK

Final Exam - details

The final examination is scheduled for 8:00-10:00AM on Tuesday, December 16 in SMTH 108 (same room as for Exams 1-3).

The exam will be comprehensive, covering topics over the entire course. There will be five questions: three full-length questions and two short calculations/short answer questions. 

The full length questions will cover:

1. Newton-Euler equations (particles and/or rigid bodies)
2. Work-energy or impulse-momentum equations (particles and/or rigid bodies)
3. Vibrations: EOM and forced response

Sample exam questions 18-35 are related to the material covered on the full-length problems on the exam. Video solutions for these sample exam questions along with Solution Video Modules related to this same material are provided through the links below. Or, just use the usual links. Links to the homework problem solution videos are found on the Homework page link on the left side of the blog.

Each short calculation/short answer question has five parts. The short calculation/short answer problems cover all material in the course EXCEPT 2D and 3D moving reference frame kinematics.

Click here for the cover and equation pages for the final exam.

_____________________________________________________

Sample Exam Solutions: Use scrollbar to locate video; click on image to view video.

Solution Video Modules: Use mouse to turn pages; click on image to view video.

Sample Problem 30

In this problem, Points C and B are related by a cable. Doesnt this mean that aBx=aCx?

And this way there s no such thing as alpha(BC).

Thank you.

Final Exam - Monday help session

We will have a help session this evening at 7PM in Room ME 155. I will stay as long as you guys have questions.

As I stated in an earlier post today, the Tutorial Room will be open from 10AM-1PM today.

Best wishes in your final exam preparation. Please keep asking questions on the blog as you study.

Sample Problem 18

Just to avoid confusion for everyone looking at this video, i think all the sins in this problem should be cosines and vise versa.
The angle theta given in this problem is the complement of the angle we usually have, i guess proff. krousgrill didnt look at that.

In case i m wrong pls let me know.
thanks
Nour

Problems with Homework Solution Videos

I already mentioned to Professor Krousgrill that the six homework solution videos listed on the homework page (7/10, 7/15, 7/19, 7/21, 7/24, 7/27) are not working, because there is no link to any one of them. However, I also noticed problems with four other homework videos. They are as follows:

- 5/197: No video available in the first place (not even listed)
- 3/189: Also no video available
- 6/109: Video isn't downloadable
- 8/67: Video "not found" (URL not found on this server)

Has anyone else had problems with these? I noticed, also, that there was only an animation for problem 2/220 and not a video, but this doesn't look way too difficult to solve, so I figured that no video was put there on purpose. Just thought I'd ask, I hope that at least the others besides 6/109 get taken care of soon, I can watch 6/109 online if need be, I really want to check all my answers and my work and make sure I have everything correct!

A simulation related to Problem 8/72

In today's lecture, we talked about how the amplitude of response depends on the ratio of omega/omega_n in base-excited systems (such as Problem 8/72):

• For small omega/omega_n, the response tracks closely with that of the base.
• For omega/omega_n near 1, near-resonance (large response) is expected. This is usually undesirable for obvious reasons.
• For large omega/omega_n, the response is diminished as compared to the base motion. This is usually good.

One way to make omega/omega_n small is to increase the value of the excitation frequency omega. For Problem 8/72, this means driving fast. This is undesirable since, as was pointed out in class, this creates a large transmitted force in the suspension (and possible an undesirable ticket from the police!). Another way to make omega/omega_n large is to decrease the value of omega_n. Note that omega_n can be decreased by INCREASING the apparent mass of the system. This is called "vibration isolation".

Earlier in the system, Ryan (rvanklom) posted an interesting idea in vibration isolation for Formula 1 vehicles called an "inerter" (see the following post). This inerter allows for the apparent mass to increase without a large increase in actual mass (it converts translational motion into rotational motion).

Shown below is a simulation of the response of one quarter of the body of a car without and with an inerter. Carefully compare the two responses. 

• As you can see, the response with the inerter is less than half of that response without the inerter. 
• Also note that the damping ratio has also decreased with the inerter (the transients take longer to die away) although the damping constant c is unchanged. Do you know why this is true? (Look at how the damping ratio is related to the damping constant and the mass of the system.)

Let us know if you have any thoughts on this.

An "inerter" and vibrations (posted for rvanklom)

Ryan has provided us with another blog challenge topic. This time it is related to a new idea for vibration control in the suspension of Formula 1 racing cars. This device is called an "inerter" that adds effective mass to the suspension system through the conversion of translation motion into rotational motion.

Click here to see the analysis provided by Ryan for the inerter.

What do you think? Do you follow his analysis?

Vibration modeling of guitar strings (posted for Dale Szul)

See attached file for a single degree of freedom model for the vibration of a guitar string. This work focuses on determining the value for the string mass to be used in the model so that the natural frequencies match up with those of the physical string.

Student Generated Solutions

The following are solutions for textbook problems written by students in the course:

• Problem No. 2/216 - submitted by Derek
• Problem No. 3/7 - submitted by RyanA
• Problem No. 3/24 - submitted by RyanA
• Problem No. 3/50 - submitted by Derek
• Problem No. 3/54 - submitted by Imtiaz Ahmed
• Problem No. 3/56 - submitted by Imtiaz Ahmed
• Problem No. 5/59 - submitted by Steve-O
• Problem No. 5/66 - submitted by Leonard Pinto
• Problem No. 5/81 - submitted by Leonard Pinto
• Problem No. 6/118 - submittted by Bradle Harner
• Problem No. 6/129 - submitted by Anonymous
• Problem No. 6/148 - submitted by Anonymous
• Problem No. 8/1 - submitted by Robert Shingleton
• Problem No. 8/3 - submitted by Robert Shingleton
• Problem No. 8/14 - submitted by Robert Shingleton
• Problem No. 8/19 - submitted by Dale Szul
• Problem No. 8/26 - submitted by Madhi Alhasan
• Problem No. 8/32 - submitted by Warren
• Problem No. 8/45 - submitted by Madhi Alhasan
• Problem No. 8/50 - submitted by Warren
• Problem No. 8/65 - submitted by Warren
• Problem No. 8/66 - submitted by Warren
• Problem No. 8/74 - submitted by ayu_djaputra

[Disclaimer: I have not yet checked through the details for all these solutions. Let us know if you find any errors. CMK]

Spring-Mass Simulator

This is a MATLAB program that simulates how a mass acts under the influence a spring system. It takes inputs derived from the EOM and outputs an XY plot of time (x axis) vs. displacement of the mass (y-axis). I suggest using EOM's from homework problems.

To use the simulator, right-click to download both files (SpringSim.m and SpringSimulator.mdl ) and put them in the same directory. Then start MATLAB and run the script called "SpringSim". The simulator should explain the rest.

I used MATLAB to create the interface and Simulink to create the simulator itself, which is the block diagram you will see when you run the program. If you have any questions about how it works or have any problems using the simulator, please comment.

NOTE: This simulator will work with any inputs, however the results may not show up on the XY plot if the applied force is substantially bigger than the product, k * (max value of displacement). If you run the simulator, don't receive an error, and nothing shows up on the XY plot, you need to use different values.

Critical Frequency - Tacoma Narrows Bridge Collapse

Here is a short documentary on the Tacoma Narrows Bridge (courtesy of YouTube). It is very interesting to see how the critical frequency can play a role in design. The bridge suffered a collapse when steady winds at the critical frequency caused the bridge to oscillate up and down before ultimately destroying it. As in class, whenever an object is being oscillated at the critical frequency, the oscillations keep getting larger and larger. Just thought it might be interesting since it covers the same topics as we have been covering in lecture.

Homework Problem 8/72

I'm having some trouble understanding somethings with problem 8/72. First, it says the mass of the trailer is 500 kg, and that each 75 kg added to the load during the loading caused the trailer to sag 3 mm on its springs. Is the 500 kg the mass of the trailer itself (i.e. without any 75 kg additions to the load), and how many 75 kg additions were added to it? And how do each of those 3 mm amounts that the trailer sags from each addition affect the problem?
Also, how do we find omega for the trailer? Are we supposed to divide the speed of the trailer (25 km/hr) by the "wavelength" between two bumps on the road (1.2 m)? I would assume omega is necessary in solving the problem, I don't see how it wouldn't be if the contour of the road is a sinusoidal function.

Homework Problem 8/67

I worked through this problem but I had the coefficient of y as 2k/m, not 4k,m. For my FBD I had two forces of k(y-y_b), going up. This gave me the right result for the term in front of y_b, but not for the term in front of y. Ideas?

Homework Problem 8/61

I am having trouble understanding exactly what 8/61 is asking exactly. I solved for "A" which is the amplitude. I then set this equal to less than 2b and solved for omega. I tried to compare this to omega_n but still wasn't completely understanding the question.