Final exam - posted solution and average

Click here for a PDF of the final exam solution. Let us know if you have questions related to the exam solution.

The mean for the final exam is 72.7%.

Best wishes for the rest of the summer and upcoming semester.

EAN and CMK

geosynchronous orbit

This reminded me of the discussion we had during lecture about satellites:
Wired News Blog
http://blog.wired.com/wiredscience/2008/08/spacex-falcon-1.html
(they mention that the orbital angle is inclined 9 degrees.. presumably from the equator?)

More info:
Geostationary
http://en.wikipedia.org/wiki/Geostationary
Geosynchronous
http://en.wikipedia.org/wiki/Geosynchronous_orbit

Enjoy!

Final Average and office hours?

Will we know the average on the final? Also, when would office hours be next week?

Graded Final

Will we be able to pick up our final exam or find out our score after it has been graded?

Professors Krousgrill and Nauman..

Thank you for a great semester! You guys are awesome.

Exam Preperation

"Those who have knowledge, don't predict. Those who predict, don't have knowledge. "

--Lao Tzu, 6th Century BC Chinese Poet

I predict this exam will be a great celebration of the knowledge i may or may not have.

-An object in motion will be heading in the wrong direction.
More funny Gerrold's First Law of Infernal Dynamics quotes

***

-"80% of the final exam will be based on the one lecture you missed."

-"The more studying you did for the exam, the less sure you are as to which answer they want."

-"An object at rest will be in the wrong place."
More funny Gerrold's Second Law of Infernal Dynamics quotes

"Complex problems have simple, easy to understand wrong answers. "

" When working toward the solution of a problem, it always helps if you know the answer. "

Just a little humor before the exam

In the vibrations example we worked through yesterday in class, on the D-axis of the graph, why does our plot intercept that axis at b/2? I may have copied something down wrong, but I'd just like to know how we determine where the graph intercepts that D axis.

-Ben

Spring Problem Question

On problem 3 of the practice final exam (the spring problem), what do they mean by the amplitude of response at resonance. Is this the same as the steady state response??

Problem 6.125

I was doing out this problem for practice and was wondering why the wheel attached to the end of the links doesn't effect the answer? I would assume that a really heavy wheel with a large MMI would cause the angular velocity to be decreased, but this doesn't seem to be the case. The only thing i can think of is that once the wheel is rolling the force propels the wheel without slowing down the links, but that seems like a pretty out-there assumption. I used Work-Energy so i assumed the velocity of the wheel would be included but it isn't.

Kinematics Question

For any disk with a no-slip contact point, c, in contact with a stationary object, is it ever possible for the contact point, c, to have an acceleration in a direction other than towards the center of the disk?

I know that if the disk is released from rest, the acceleration towards the center will be zero.

So does this mean that the acceleration of the contact point in any direction would be zero if released from rest?

Final Exam - details

Click here to download PDF of some final exam details provided in today's lecture.

Professor Nauman and/or I will be around most of tomorrow if you have questions.

Best wishes in your exam preparation.

Homework!!!

Is our homework assignment due tomorrow?

Are you going to post a solution guide to for the practice exam?

Final exam - cover and equation sheets

Click here for a copy of the cover and equation sheets for the final exam.

Practice final exam copy

Click here to download a copy of the practice final exam from Monday evening.

Let us know if you have questions on this practice exam.

Practice final exam - reminder

The practice final exam will be given this evening from 6-8PM in Room ME 261. We plan to grade the practice exams immediately after the exam is over. If you want to see our feedback this evening, you can return to the room between 10:00-10:30PM. Otherwise, you can pick it up in tomorrow's class.

The intent of the practice exam is to give you an opportunity to get feedback from us on your work. If you feel that this will help you in preparing the final of Wednesday, we welcome you to participate. If not, that is OK, too. You are the best judge as to how you learn.

Problem 8/48

I am having problems solving for the amplitude for the damped part of the problem (c = 500).

The book gives a direct equation for this amplitude on p. 623 (eqn. 8/20). Is it acceptable to go straight to this equation?

If not, when you assume a solution of x = X_1*cos(omega*t) + X_2*sin(omega*t), both X_1 and X_2 will be nonzero. How do I find a single amplitude using both X_1 and X_2?

If you assume a solution of x = X*sin(omega*t - phi), I get stuck when plugging x, x_dot, and x_dot_dot back into the EoM. The left side of the equation has coefficients of cos*(omega*t - phi) and sin*(omega*t - phi) while the right side is simply F_0*cos(omega*t). How do I equate coefficients to solve for X?

Problem 8/72

Steps:

1. FBD: shown above for trailer (pay close attention to the magnitude and direction of the spring force on the trailer).
2. Newton/Euler: sum F_x = k(y_B - x) - mg = m*x_dot_dot
3. Kinematics: The position of the trailer, z, is given by z = v*t since the trailer moves at a constant speed. The vertical position of the wheel B depends on the position z of the wheel along the road; that is y = y(z). It is your task to write out y(z) as a sinusoidal function (use either a cosine or sine) based on the known wavelength (1.2 meters) and amplitude (0.05/2 meters). Substituting z = v*t into this equation for y gives y = y(t). From this you can identify the frequency omega of the excitation.
4. Solve: You are asked to find the steady-state response of the trailer x(t) as a function of time. However, in actuality, you only need to know at what frequency omega the response is the greatest (hint: this occurs at resonance). That is, you need to set omega = omega_n.

Note that you are not directly given the stiffness of the spring for the suspension of the trailer. What you are given is the increase in static deformation of the suspension (0.003 meters) under additional loading on the trailer (75*9.806 newtons). From this, you can find k.

Let us know if you have questions on this.

Problem 8/61

Steps:

1. FBD of block: pay careful attention to both the DIRECTION and MAGNITUDES of the spring forces acting on the block that are shown in the FBD above.
   
2. Newton/Euler: sum F_x = 2*(k/2)*(x_B - x) = m*x_dot_dot
   
3. Kinematics: none needed
4. Solve: Note that the "base excitation" here provides a prescribed motion of the box as a function of time. In your EOM in 2., this is an "inhomogeneous" term that is harmonic with a frequency of omega. Solve for the steady-state response for x(t) = X(omega)*sin(omega*t). Make a sketch of X vs. omega. From this determine the ranges of omega over which the absolute value of X is less than 2*b.
   

CORRECTION on Step 4. above. We are asked to make the amplitude of the motion of the block RELATIVE to the box less than 2*b. The motion of the block relative to the box is given by z(t) = x(t) - x_B(t), not x(t). Use your result for x(t) in Step 4. to find z(t) = (X - b)*sin(omega*t). Make a sketch of X - b as a function of omega, and from this, find the ranges of omega over which the magnitude of (X - b) is less than 2*b. Sorry for any confusion created by my above hint. Again, I did not read the question very closely.

Let us know if you have questions on this.

Final exam preparation

ME 274 students,

Please note that the final exam for ME 274 will be 3:20-5:20PM on Wednesday, July 30 in ME 161. We will be providing details on the coverage of the final early next week in lecture.

We will NOT be having a review session for the final exam. However, the Tutorial Room will be open during regular hours on Monday and Tuesday of next week. We will also have extra office hours during the early part of the day on Wednesday.

We will be offering an opportunity on Monday evening to assess your level of readiness for the final exam. During a two-hour period on Monday evening (time and location TBA) we will offer to interested people the opportunity to take a sample final exam. After completing the exam, we will grade your exam to give you feedback on how you did. The score will not count toward your grade; rather it will help you determine where you have weaknesses and on what topics that you should focus as you study. Participation is not required; do so only if you want the help. If you are interested in participating, please either leave a comment (including your name) on this post, or send me an email. We would like to know the level of interest in this prior to Monday evening.

Best wishes,

EAN and CMK