Iterative Prediction of Spring-Mass System

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{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math]

[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]

In order to update the object's velocity and position, similar equations can be used:

Velocity Update Formula:

[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

Examples

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