A Journal of Applied Mechanics & Mathematics, #49
A Bad Example
Most of us are inclined to trust an established textbook. We assume (1) the author knows what he is talking about, (2) the book has been carefully vetted by several editors and reviewers, and finally (3) the fact that it is well established in the market means that thousands of other readers have tacitly endorsed it as well. While these assumptions are usually true, they are no guarantee, and they can and do fail us at times. The topic of this post is one such failure. Beware!!
The format of engineering textbooks is fairly uniform, consisting of alternating sections of Theory and Examples. For a student encountering the material for the first time, the Theory is often simply too much, and blows right over the head of the student. The starting student relies heavily on the Examples to comprehend, even if incompletely, what the material is about. The Theory is most useful when the material is studied a second or third time in some depth. Because many will only study the material a single time while in college, it is critically important that the Examples be correct and in no way misleading. Sadly, both of these problems exist in the book discussed here.
The book in question here is Mechanical Vibrations by S.S. Rao, where both the book and the author are well known. The book was published early by Addison-Wesley; I have a 2nd edition dated 1990. It has been re-published more recently by Pearson in a 6th edition with a 2018 copyright date. The problem shown in the Figure is used in both of these, with only very minor changes. The same errors exist in both versions, indicating that in 28 years, Rao has learned nothing about this simple statics problem.
I encourage all readers to examine carefully the discussion in t he attached paper. It demonstrates clearly that even the experts go badly astray at times.