PAGE EDITOR(S): Omar Jarrett, Jake Russin, Jeremy Fryd, Matt Nostro
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Here's a cool website with a lot of simple animations to better understand Simple Harmonic Motions and how the sin/cosin graphs fit in.

http://www.acoustics.salford.ac.uk/feschools/waves/shm.htm

This one also has some dynamite figures:
http://www.animations.physics.unsw.edu.au/jw/SHM.htm

Simple Harmonic Motion Equations

The motion equation for simple harmonic motion contains a complete description of the motion, and other parameters of the motion can be calculated from it.
external image shm2.gif
external image sprmass.jpg
external image shm3.gif
The maximum velocity and acceleration are given by
external image shm4.gif
The total energy for an undamped oscillator is the sum of its kinetic energy and potential energy, which is constant at
external image shm5.gif



Here is a really interesting and relevant video that explains exactly how Simple Harmonic Motion works:
http://www.youtube.com/watch?v=MdmbkeJe6zohttp://www.popsci.com/breakdown/article/2008-07/ancient-bungee-jumping

Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. The motion is sinusoidal in time and demonstrates a single resonant frequency.
Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. The motion is sinusoidal in time and demonstrates a single resonant frequency.


The motion equation for simple harmonic motion contains a complete description of the motion, and other parameters of the motion can be calculated from it.
external image shm3.gif

The velocity and acceleration are given by

external image shm4.gif
The total energy for an undamped oscillator is the sum of its kinetic energy and potential energy, which is constant at
external image shm5.gif
----external image SHM1.gif
Here is the link to the image's website
This image is pretty similar to the one that Mr. Natland draws on the left side of the board all the time. At the top, the spring is being stretched out so the spring is pulling it back towards the equilibrium point. At this point, the force exerted by the spring is greatest and the acceleration of block is also greatest, assuming that this it is at its amplitude. As the block gets pulled back, the force exerted by the spring on the block decreases according to the equation (spring force)=kx, where x is . When the object passes throught the equilibrium point during the oscillation, its velocity is at a maximum and its acceleration is at 0.
Then when the block continues to the left of the equilibrium point, the force of spring pushes the other way, towards the equilibrium point. The reason that it continues to move to the left even though the net force is to the right is because it has kinetic energy. As it goes to the left, it slows down and the kinetic energy is converted back to spring energy.

D012_Incense039.jpg
This video shows a large pendulum used to disperse incense in the Cathedral of Santiago de Compostela in Galicia, Spain.
http://www.caminodesantiago.me.uk/santiago-cathedral-botafumeiro/


Online quiz
Useful Pictures, Videos, and Websites

http://www.animations.physics.unsw.edu.au/jw/SHM.htm
(Nice animation of the SHM of an oscillating vertical spring)

http://www.youtube.com/watch?v=bPtlRf6dg8c&feature=related
( Simple harmonic motion in three minutes!)

http://www.splung.com/content/sid/2/page/shm
(lays out formulas of simple harmonic motion really well)


Slinky+Jim Carrey+Buddhist Tempel= SHM

Links:
http://www.walter-fendt.de/ph11e/pendulum.htm
(At the above link, you can change the length, mass, and amplitude for a pendulum and see how the period changes.)

http://www.walter-fendt.de/ph11e/springpendulum.htm
(At the above link, you can change the spring constant, mass, and amplitude of a spring, and see how it changes the acceleration, velocity, and energy.)

Practice Problem:
1. http://apcentral.collegeboard.com/apc/public/repository/ap09_frq_physics_b.pdf


SOURCES
http://apcentral.collegeboard.com/apc/public/repository/ap09_frq_physics_b.pdf
(For AP problem)