Iterative Prediction of Spring-Mass System: Difference between revisions

From Physics Book
Jump to navigation Jump to search
No edit summary
No edit summary
Line 16: Line 16:
<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>


<div style="text-align: center;"><math>{\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{&Delta;t}}</math><div>


<div style="text-align: center;"><math>{\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{&Delta;t}}</math><div>
<math>{\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{&Delta;t}}</math>
 
 
<math>{\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{&Delta;t}}</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{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math]


[math]\displaystyle{ {\vec{p}_{f} - \vec{p}_{i} = \vec{F}_{net}{&Delta;t}} }[/math]


[math]\displaystyle{ {\vec{p}_{f} = \vec{p}_{i} + \vec{F}_{net}{&Delta;t}} }[/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}}{&Delta;t} }[/math]

Position Update Formula:

[math]\displaystyle{ {\vec{r}_{f} = \vec{r}_{i} + \vec{v}_{avg}{&Delta;t}} }[/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

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Middling

Difficult

Connectedness

  1. How is this topic connected to something that you are interested in?
  2. How is it connected to your major?
  3. Is there an interesting industrial application?

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

Internet resources on this topic

References

This section contains the the references you used while writing this page