Iterative Prediction of Spring-Mass System: Difference between revisions
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<div style="text-align: center;"><math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math><div> | <div style="text-align: center;"><math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math><div> | ||
< | <math>{\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}}</math> | ||
<math>{\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}}</math> | |||
Revision as of 13:55, 1 December 2015
claimed by kgiles7
Short Description of Topic
The Main Idea
A simple spring-mass system is a basic illustration of the momentum principle. The principle of conservation of momentum can be repeatedly applied to predict the system's future motion.
A Mathematical Model
The Momentum Principle provides a mathematical basis for the repeated calculations needed to predicts the system's future motion.
The most useful form of this equation is referred to as the "momentum update form" of the Momentum Principle, and can be derived as shown below:
[math]\displaystyle{ {\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{Δt}} }[/math]
[math]\displaystyle{ {\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{Δt}} }[/math]
[math]\displaystyle{ {\vec{v}_{f} = \vec{v}_{i} + \frac{\vec{F}_{net}}{m}}{Δt} }[/math]
Position Update Formula:
[math]\displaystyle{ {\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{Δt}} }[/math]
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
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