Bill Goodwine's Courses

Reading assignment: Chapter 4.

Problems: 4.2, 4.3, 4.4, 4.5, 4.6, 4.11 and 4.12.

For problem 4.2 part 1 do we have to solve for the whole solution or just the steady state solution? If we have to solve for the entire solution, I understand that the homogeneous solutions are different for each case, but do we have to solve for c1 and c2 everytime?

mbrundag wrote:For problem 4.2 part 1 do we have to solve for the whole solution or just the steady state solution? If we have to solve for the entire solution, I understand that the homogeneous solutions are different for each case, but do we have to solve for c1 and c2 everytime?

Yes. It's not that much work since the homogeneous solutions are given in the chapter. You just need to find the particular solution for a sine forcing function, then evaluate the c's for each case. If a term is complicated but repeated, then maybe just substituting a symbol for it in the computations will save some ink.

In graphing part 3 of 4.2, I get a graph that appears the same as the graph found on page 100 (which I presume to be correct) except that my graph has its max near 2.5 while the one in the book has it located at about 6.5. I cannot find an error in my work. I'm wondering if you could verify that it should look like the graph on page 100 or tell me that i have a mistake.

Related to that, problem 4.3 requires use of that graph and will obviously give me different answers if i use my graph as opposed to the one in the book.

tmalecek wrote:In graphing part 3 of 4.2, I get a graph that appears the same as the graph found on page 100 (which I presume to be correct) except that my graph has its max near 2.5 while the one in the book has it located at about 6.5. I cannot find an error in my work. I'm wondering if you could verify that it should look like the graph on page 100 or tell me that i have a mistake.

Related to that, problem 4.3 requires use of that graph and will obviously give me different answers if i use my graph as opposed to the one in the book.

I think that the graphs should be the same -- the magnitude shouldn't matter if it is a sine or cosine. There is always the possibility that I mis-labeled the graph, but I was typically pretty careful about those things since I don't really want to have to re-do them. The height of the peak is very sensitive to the damping ratio: the difference between .15, .1, 0.5 etc., may be huge.

I get the same graph as tmalecek for the magnification factor. If I remove the square root from my expression for M, I get the graph in the book.

avalenzu wrote:I get the same graph as tmalecek for the magnification factor. If I remove the square root from my expression for M, I get the graph in the book.

Thanks. I suspect your's are right and the book is missing a sqrt().

In problem 4.2 part 3, we are supposed to plot the magnification factor versus w/wn. In Figure 4.16, the denominator is wrong. Shouldn't it be (1-w^2/wn^2)^2 ?

Yes, plot it versus w/wn.

Also, yes, that's a typo in the label for the figure.