Odesolve failure - Kenneth Macfarlane

[AlanStevens]

See attached.

Alan

[ptc-6286072]

Ace. How did you learn this?

Ken

[AlanStevens]

Trial and error mostly!!

Alan

[ptc-6286072]

Alan

I used Mathcad (thanks to you) trying to obtain confirmation of my results from theory according to Dynamics, by J.L. Meriam, and another source from an internet search. Both the theoretical resutls match each other using different equations, but Mathcad gives different answers (see attached worksheet). Any views on this?

Ken

[AlanStevens]

I can't see anything wrong with the Mathcad calculations. I've tried it a couple of other different ways (as two simultaneous first-order equations for y and v, for example, and even as a simple Euler integration!) and get the same solutions. I don't know how the text book authors got their results, so it's difficult to comment. My best guess is that there is a difference in the input data somewhere, but I don't have the book data to check.

Alan

[ptc-6286072]

Alan

Dynamics, 7th edition, is available as a free download using the following link:

http://www.ebooksdownloadz.com/2014/01/engineering-mechanics-dynamics-7th.html

Ken

[AlanStevens]

I've looked at this now, and although page 602 gives the ODE, I can't see either the data you've used or the graphs you included in the worksheet!

Alan

[ptc-6286072]

Alan

I used a lot of graphite and scrap paper to work this one out. You'll find Sample Problem 8/2 on page 592 useful, together with equations (8/20), (8/21), (8/22), and the damped natural frequency on page 590. Hope you get the same answers.

Ken

[AlanStevens]

Using your data and the equations in the text book I get the same results as Mathcad's ODE solver - see the lower section of the attached worksheet.

Alan

[ptc-6286072]

Alan

I've realised that the Odesolve_Test file I sent on 18 July had a different spring stiffness from the results I added on 21 July. I reconciled this on the attached updated version of Odesolve_Testb. x(t=.011)'s now match exactly. On my chart 0.4918 is the maximum velocity in the range 0 < t <.011 which of course doesn't match your v(t=.011), but my v(t=.011) is now a perfect match. You've boosted my confidence big time in my results, and for using Mathcad as an alternative. Much appreciated.

Ken