EJSS simple harmonic motion pendulum model with t vs
based on models and ideas by
- lookang http://weelookang.blogspot.sg/2014/02/ejss-shm-model-with-vs-x-and-v-vs-x.html
- lookang http://weelookang.blogspot.sg/2010/06/ejs-open-source-simple-harmonic-motion.html?q=SHM
- lookang http://weelookang.blogspot.sg/2013/02/ejs-open-source-vertical-spring-mass.html?q=vertical+spring
- lookang http://weelookang.blogspot.sg/2010/06/physical-quantities-and-units.html?q=pendulum
- Wolfgang Christian and Francisco Esquembre http://www.opensourcephysics.org/items/detail.cfm?ID=13103
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| commons terms associated with pendulum http://en.wikipedia.org/wiki/File:Simple_gravity_pendulum.svg#file |
Assumption of this simple pendulum model:
- The rod or cord on which the bob swings is massless, inextensible and always remains taut;
- The bob is a point mass;
- Motion occurs only in two dimensions, i.e. the bob does not trace an ellipse but an arc.
- The motion does not lose energy to friction or air resistance.
Assumptions of SHM comparable to pendulum:
- Motion approximates SHM when the angle
θ of oscillation is small, wheresinθ≈θ
The equations that model the motion of the pendulum system are:
where the terms
If the motion starts to the positive amplitude position:
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General Rule of Thumb
Thus, in general, the pendulum's swing motion is
approximately a simple harmonic motion only when the Motion's angle θ
of oscillation is small, where sinθ≈θ ,
rule of thumb is about 5 degree!