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 Ratings
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| Reviewed: |
Mar 28, 2007 by Physics |
| Overview: |
This applet is a java simulation that enables the user to observe simple harmonic motion by way of a simple pendulum. The user can start, pause/resume, and reset the simulation at any time. Furthermore, the user can change the values for the length of the pendulum, the mass at the end of the pendulum, the amplitude, and the acceleration due to gravity. A Slow motion feature is available to observe the motion in more detail. The graphs of the position, velocity, acceleration, force, and energy (both kinetic and gravitational potential) vs. time are available. The graphs are only available one at a time but the user can change between them very easily. A clock is displayed at the bottom of the screen along with the period (T). The current position (x) along with the maximum position is displayed at the bottom of the position vs. time graph and likewise for the velocity, acceleration, force, and energy graphs. The vector arrows are displayed on the velocity, acceleration, and force graphs. A bar graph is displayed on the energy graphs. The user is able to check the values for these quantities using the equations derived for simple harmonic motion. The simulation will only allow small amplitudes (i.e. much less than 1 radian) thereby permitting simple harmonic motion. |
| Learning Goals: |
To help understand the qualitative and quantitative aspects of simple harmonic motion by way of a simple pendulum. |
| Target Student Population: |
High School or introductory College courses of all types |
| Prerequisite Knowledge or Skills: |
Some knowledge of the vocabulary regarding Simple Harmonic Motion and Pendula, for example, knowing what period, amplitude are for such motion. The ability to read and interpret graphs, such as velocity or acceleration vs. time, etc. would be of significant benefit |
| Type of Material: |
Java Simulation in a Browser Window. |
| Recommended Uses: |
In-class demonstration, self-study, supplement to in-class material, building block for an assignment or virtual laboratory |
| Technical Requirements: |
JAVA enabled browser |
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| Strengths: |
This is a basic simulation of a simple Pendulum within the small amplitude approximation. The calculation of the period of the oscillation is accurate within that approximation. The amplitude has a maximum value of 20 degrees which is much less than one radian. The graphs are accurate as well as the clock.The vector arrows on the velocity, acceleration, and force graphs were correct along with the bar graphs for the kinetic and potential energies. |
| Concerns: |
It appears that the small amplitude approximation is being used for the simulation; rather then the non-linear equation solution. The author limits the user to a maximum amplitude of 20 degrees. This limitation is appropriate, given the small amplitude approximation. One reviewer calculated that the small angle approximation introduces an error of 0.76% in the period for a 20 degree amplitude. While relatively minor, this would just be noticable given the accuracy of the period displayed by the applet, i.e. within a thousandth of a second.
The other reviewer found one discrepancy in the gravitational potential energy. On one example, the PE was calculated to be 4.35 J and the simulation calculated 4.40 J. The difference was probably in the value for h, the distance the bob was above the starting location.
These are minor in nature, and one could be alleviated by indicating clearly that the simulation is using the small amplitude approximation. |
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Potential Effectiveness as a Teaching Tool |
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| Strengths: |
This applet is very versatile! It can be used to check homework problems assigned by a teacher, reinforce material discussed in class, an in-class demonstration, or possibly a virtual laboratory. Furthermore, it provides an excellent qualitative analysis of simple harmonic motion as well as a quantitative approach. Graphs are readily and accurately displayed on the screen. The vector arrows are displayed on the velocity and acceleration graphs which help reinforce the concept of when an object speeds up the velocity and acceleration have the same direction and opposite if they are slowing down. The vector arrow on the force graph is helpful to reinforce Newtons 2nd Law whereby the direction of the net force is always the same as the direction of the acceleration. The bar graphs on the kinetic and gravitational potential energy graphs are very useful to help display the law of Conservation of Energy. There are several variables the user is able to change thereby creating a very good control of variables exercise. |
| Concerns: |
Since the small angle approximation is used; one can not use this applet to investigate the limitations of the small angle approximation. The authors display the period to 3 significant digits past the decimal point. Deviations from small amplitude behavior would show up in the last digit at about 8 degrees of amplitude. |
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Ease of Use for Both Students and Faculty |
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| Strengths: |
This applet is rather straight forward to use. I was able to determine all of the features in a relatively short amount of time. The author provides some helpful instructions and comments at the top of the page. The ability to change from position to energy to force, etc. is seamless. The user has the option to pause and restart at any time as well as running the simulation in slow motion (i.e. 10 times slower). A digital clock displays the time. The values of the instantaneous position, velocity, acceleration, force, and kinetic and gravitational potential energies are continuously displayed along with the maximum values. The graph keeps running continuously with the updated times at the bottom. |
| Concerns: |
The length of the pendulum has a limit of 10 meters. There is no zero (0) elevation point labeled in the graph. There is no Step feature available which would help the user to stop the simulation at any time to record accurate data. |
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