I need to find 5 different examples of SHM and the governing equations besides springs and pendulums. I must be looking in all the wrong places. I have found articles about rocking chairs, swings, and sound waves, ocean waves etc but don't find governing equations and I am not even sure if they are still simple, help please?

The governing equations for the springs and pendulums can be found at standard textbook or on the web (Have you try to search at wikipedia). you will find SHM motion, if there is a small enough deviation from stable static equilibrium. For example: touch the water surface lightly, knock the drum surface...

I guess it is your homework, so you should try to find out the answer by yourself. What you need is knowing what is SHM and looking at everything around you more carefully. And you will find many examples.

My issue is what constitutes "different" since shm is all the same? Aren't they all isomorphic to each other? Then they are not different. Also everywhere I read someone is talking about shm and then they deviate and then I am not sure where they began to deviate. For example I know that shm is periodic and that the frequency is constant. The velocity of the oscillator is maximum as it passes thorgh equilibrium and zero as it passes through the extreme positions in it's oscillation. I know there is always a restoring force which always acts toward the equilibrium position. The acceleration is directly proportional to the displacement from the equilibrium position. So you see I have done my homework. I know shm is in springs, pendulums, waves, molecules, Lc circuits. I just wanted to know more than that and how to discern when a writer has deivated from shm, that's all. And oh yeah, I am a graduate student and this is paper I am researching so it's not homework. PS Your spell check is not working, blank screen that says it is done.

Sorry! There is no way I can know your background and what is the purpose for your post. There are students just post their homework and want someone to answer it for them.

Since you are a graduate student, I am going to assume your are aware of Tayler's expansion. We can define a potential for an equilibrium system (SHM is a small deviation from an an equilibrium). U(x)=U(x0)+ dU/dx|_{x=x0} (x-x0) + (1/2!) d^{2}U/dx^{2}|_{x=x0} (x-x0)^{2}+(1/3!)d^{3}U/dx^{3}|_{x=x0} (x-x0)^{3}+ ... F=-dU/dx ,so

Fx=- dU/dx|_{x=x0} - d^{2}U/dx^{2}|_{x=x0}*(x-x0) -(1/2!)d^{3}U/dx^{3}|_{x=x0} (x-x0)^{2}-... =- d^{2}U/dx^{2}|_{x=x0}*(x-x0) -(1/2!)d^{3}U/dx^{3}|_{x=x0} (x-x0)^{2}-... (because dU/dx|_{x=x0}=0 at equilibrium point x0)

If the higher order term is smaller compared to the first term, the above equation reduced to Fx=- d^{2}U/dx^{2}|_{x=x0}*(x-x0) = -k *(x-x0) That is the reason why a small deviation from the equilibrium will show SHM motion if the higher order term is smaller(can be neglect).

For a small wind, the leave on the tree will show SHM motion. For a stronger wind, branch of the tree will show SHM motion. For a hugh wind, the whole tree might show SHM motion.

Since you are a graduate student, I will leave the rest to you to think about it. And you will learn something from it.

Thank you for tell me there is something with the spell check function.

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...

Its really nice to have some one interested in physics and helping students to explore there knowledge in physics. This is the first time i am using these stimulations hope i can present them in a very effective and convinciable way to my students......Being a teacher for +2 students i trying to give them a very convinciable presentations, can you please help me out in presenting topics like periodic motion and when it becomes shm.

I reckon the rather dry word oscillate may become a bit less dry when we learn its story. It is possible that it goes back to the Latin word ōscillum, a diminutive of ōs, “mouth,” meaning “small mouth.” In a passage in the Georgics, Virgil applies the word to a small mask of Bacchus hung from trees to move back and forth in the breeze. From this word ōscillum may have come another word ōscillum, meaning “something, such as a swing, that moves up and down or back and forth.” And this ōscillum was the source of the verb ōscillāre, “to ride in a swing,” and the noun (from the verb) ōscillātiō, “the action of swinging or oscillating.” The words have given us, respectively, our verb oscillate, first recorded in 1726, and our noun oscillation, first recorded in 1658. The next time one sees something oscillating, one might think of that small mask of Bacchus swinging from a pine tree in the Roman countryside. Yes.

Hi. I have installed this software but after the installation i faces lots of problem. Now when i saw this forum i got solutions of my problems. Thanks a lot. -*-

Hi there,I just wanted to comment & say keep up the quality work.Thanks a lot for sharing. You have done a brilliant job. Your article is truly relevant to my study at this moment,and I am really happy to read it.I'm so impressed very useful. I've learned a lot from your blog. -*-