Thanks for the reply. I follow your argument and I understand what you are saying about the Taylor series expansion and that the 3rd derivative is negligible. It also makes sense that a small wind might make a leaf have shm and a little larger might make a branch have shm and a very large wind might make the tree have shm. It's kind of like the angle on a pendulum being "small" having shm and when large it doesn't. Or for the torsional pendulum when the wire is small compared to the relative largeness of the bar. By the way, I am also a math professor at a local college...

spell check still doesn't work, sorry for any typos overlooked...