based on models and ideas by

http://weelookang.blogspot.com/2014/08/ejss-shm-model-with-all-7-graphs.html EJSS simple harmonic motion model with all 7 graphs https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM/SHM_Simulation.xhtml source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHM.zip author: lookang author of EJSS 5.0 Francisco Esquembre |

- lookang http://weelookang.blogspot.sg/2010/06/ejs-open-source-simple-harmonic-motion.html?q=SHM
- Wolfgang Christian and Francisco Esquembre http://www.opensourcephysics.org/items/detail.cfm?ID=13103

The equations that model the motion of the spring mass system are:

Mathematically, the restoring force $ F $ is given by $ F = - k x $

where $ F $ is the restoring elastic force exerted by the spring (in SI units: N), k is the spring constant (N·m−1), and x is the displacement from the equilibrium position (in m).

Thus, this model assumes

$ \frac{\delta x}{\delta t} = v_{x} $

$ \frac{\delta v_{x}}{\delta t} = -\frac{k}{m}(x-l) - \frac{bv_{x}}{m} + \frac{A sin(2 \pi f t)}{m} $

where the terms

$ -\frac{k}{m}(x-l) $ represents the restoring force component as a result of the spring extending and compressing.

$ - \frac{bv_{x}}{m}$ represents the damping force component as a result of drag retarding the mass's motion.

$ + \frac{A sin(2 \pi f t)}{m} $ represents the driving force component as a result of a external periodic force acting the mass $ m $.

## What is SHM?

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. In order for simple harmonic motion to take place, the net force of the object at the end of the pendulum must be proportional to the displacement. In other words, oscillations are periodic variations in the value of a physical quantity about a central or equilibrium value.As long as the system has no energy loss, the mass will continue to oscillate. Thus, simple harmonic motion is a type of periodic motion.

## Developers' Note:

currently, seems to be compilable using system like

Win 7 x64EJS_5.0_140730

Java 7 Update 60 (64-bit)

Win 8.1 x64

EJS_5.0_140730

Java 1.7.0_67 found C:/Program Files/Java/jre7/ (32-bit)

FAILED.

Win 8.1 x64

EJS_5.0_140730

C:/Program Files (x86)/Java/jre7/