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DrD last won the day on October 13 2018

DrD had the most liked content!

About DrD

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  • Location
    Iowa, USA
  • Interests
    Kinematics, dynamics, mechanics of materials, Theory of Machines, machine design, vibrations
  • Present Company
    Machinery Dynamics Research
  • Highest Qualification
  • Engineering Qualification
    Registered Professional Engineer, TX, WI (Ret'd)

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    Consulting work for a variety of industries, particularly in the IC engine related area (Torsional vibration analysis, shaking force analysis, engine cam design, system simulation).

    Author of several books, including one widely used textbook for Theory of Machines.

    Life Member ASME
    Member SAE
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  1. Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #46 Comments on A Calculus Challenge I would like to thank all those who took part in the Challenge. My solutions and comments are attached. 46 CalcChallengeComments.pdf
  2. DrD

    A Calculus Challenge

    I'll get to you William. Please be patient. I have a few other things going on right now. DrD
  3. DrD

    A Calculus Challenge

    Dear Mucugia, The challenge is now closed, and I will not be reviewing additional work any longer. Thanks for the effort. DrD
  4. DrD

    A Calculus Challenge

    Dear Mucugia, Two problems: (1) It looks like you may have left out a page. You sent Page 1 and Page 3, but what about Page 2? (2) Neither of the pages that you sent are complete. The PDF does not show the final result on either page. You might do better to copy these pages over , writing a bit smaller so t hat the scan will capture the whole page. DrD
  5. DrD

    A Calculus Challenge

    Dear Amin, Well, I have both the 2nd and 5th editions of Roark, so I am unable to tell whether the book is correct (or if you read the book correctly). That's the problem with using a reference source (although Roark is widely recognized). I'm amused that you said, "When they ask "how do you gget formula?" the answer will be "here is the formula in the book." Does that really convince you? Are you more convinced by something in a book, or be a carefully worked out derivation that you can follow for yourself? I'll take the derivation every time!! It is certainly true that handbooks have their uses. The problem is, they also have their limitations. If there are assumptions made in the derivation, looking the formula up in a book may not tell you about those assumptions. I'm sorry that you evidently find the area moment of inertia expressions just too tedious to be worth your time. For those who want to find out if they really can use calculus, this remains a very useful exercise. DrD Dear HKS, You promised results after the New Year. Just which New Year did you have in mind? DrD
  6. DrD

    A Calculus Challenge

    Thanks for the information, Jarek. I do not like MS Word, and would never use it given any choice in the matter. But, I know many others like it, so this is useful. DrD
  7. DrD

    A Calculus Challenge

    Dear Jarek, Thanks for the comment on Mathtype. I have heard of it, but know little about it. I use LaTeX for all of my work, but I like the way your work looks very much. DrD
  8. DrD

    A Calculus Challenge

    Dear Jarek, Just as a matter of curiosity, how do you write the equations in your work? They are clearly type written, but I'm curious what software you use for this. Is it MS Word, some other word processor, or what? It looks good, but I'm interested to know more. DrD
  9. DrD

    A Calculus Challenge

    Dear Jarek, I cannot quite agree with your result. I think you may have an algebraic error in the calculation of y2-bar. I'd look there first. Interesting approach, I must say. DrD
  10. DrD

    A Calculus Challenge

    Dear Wasulia, Congratulations, you got the correct answer, almost. Two comments come to mind: (1) You made an error in factoring out R^2 in the last line; (2) You should learn that, when doing calculus, angles are always expressed in radians, so your factors 360, 180, etc are really errors. Learn to think in radians; it will help you a lot. You took the long way around, but you almost got here. Good effort. ----------------------------------------- Dear Jarek, You are correct in saying x-bar is zero. I'm amazed that no one else has seen that yet! Without saying yes or no to your result for y-bar, I have two comments for you: (1) I urge you to provide a sketch showing how you formed the integrals you offer as a route to the answer. (2) You already have an expression for the area, so I would urge you to substitute it and seek to simplify the result. DrD
  11. DrD

    A Calculus Challenge

    Dear Amin, There are a few problems with your answer. 1) If you are going to cite Roark, you should surely say which edition. There are many, and they are not all the same. I have two of them myself, but quite likely not the one you use. 2) You don't give your final result for the area. You simply cite Roark, but there is nothing here that I can check. Roark has been known to be wrong. 3) You give an answer for something you call "static moment," but you do not locate the centroid. 4) You say, "The same for moment of inertia." The same what? You have given any answer before (unless you meant your area result), so this is no answer at all. 5) You seem to think actually answering the question is beneath you because you know how to look in a book. What do you do if the book is not at hand? 6) You said, "When I had to deal with these kind of problems, I used to go to handbooks." Do you think handbooks have all the answers? Do you no longer do engineering? Overall, I'd say this is a fairly poor effort by someone who really is not very interested. DrD
  12. DrD

    A Calculus Challenge

    Well, as of now (4 Jan 2019), over 1000 people have looked at this problem, one person has worked one part of the problem statement, and another says he know how to do this without integration (and thus far, without results). You folks are real balls of fire!! DrD
  13. DrD

    A Calculus Challenge

    Dear Jarek, Your figures help a lot to explain your logic. Thank you. I'd say you definitely have the answer for the first part. Now, can you extend this to obtain the other answers ? DrD
  14. DrD

    A Calculus Challenge

    Dear Jarek, Your final result for the enclosed area is correct (if we ignore some notational inconsistency, r in place of R). Congratulations!! That said, I cannot follow your development. Would you explain your reasoning with some words, perhaps? In particular, you show the sum of two integrals equal to a third integral. How is that equality established? I cannot follow it. Also, you write in the integrand in one place xtgalpha; what is this? Is "tg" the tangent function? If so, it would help if you would enclose the argument in parentheses. Now, to all others, I hope you see that the problem is not impossible. Why are you so unwilling to try it yourself? DrD
  15. DrD

    A Calculus Challenge

    My word! An answer ... I'm simply stunned! If you are sure it can be solved without integration, go ahead. This will serve as a check on the results obtained by integration. If you use formulas from a book, please be sure to give their derivation as well. DrD