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- PP+ Force Vector Addition
- PP+ Force Vector Addition Vs. Least Squares Curve Fit
PP+ Force Vector Addition vs. Least Squares Curve Fit Utilizzo e statistiche
The Addition of Force Vectors lab uses a force table to investigate the vector addition of forces. It is part of Polyhedron Physics Plus, a set of 24 iPad apps for use in the classroom. To see how they work, try the FREE PP+ Newton’s 2nd Law lab. For those who’d prefer to develop their own experiments, the PP Force Table app features a similar apparatus without lab procedures and other supporting materials.
In addition to a 3D simulation that produces realistic data, each lab includes introductory videos, background theory, experimental procedure, analysis and reporting tools, pre-lab quiz, post-lab questions, and teacher support materials. The experimental data produced by the simulations are realistic, including random and systematic errors. These features allow students to use standard data analysis and error analysis techniques to report on their own unique data, just as if the experiment had been performed using hands-on equipment.
These labs can serve as replacements for hands-on labs, especially when equipment is not available, or as supplements to hands-on labs. They are also a suitable option for students in distance learning and home school situations. Formative and summative evaluations showed no significant difference in learning between students using the virtual labs and those using hands-on labs. Preliminary results suggest increased learning by students using the virtual labs as supplements to hands-on.
Polyhedron Physics was developed by Polyhedron Learning Media, Inc. with partial funding provided under contract numbers ED-07-CO-0040 and ED-IES-11-C-0029 from the Institute of Education Sciences in the U.S. Department of Education through the Small Business Innovation Research (SBIR) program.
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“Least Squares Curve Fit” is a user friendly, free of charge and free of ads app.
User inputs point sets and chooses function types.
Utilizing the Least Squares Linear Regression Method, the app calculates best fit curves, reports equations and draws graphs.
Point sets can be stored in a table and are available after app is closed.
Currently available function types are:
2D:
1. Line.
2. Parabola.
3. Polynomial up to 8th degree.
4. Circle.
5. Conic section (Ellipse or Hyperbola).
6. Trigonometric function as
C + A1*cos(ω*x) + B1*sin(ω*x) + … + An*cos(n*ω*x) + Bn*sin(n*ω*x),
where user can select n between 1 and 8 and enter any ω.
7. Exponential Function.
8. Bell Curve.
3D:
1. Plane.
2. Sphere.
Also, there is an option to choose the Best Fit:
the app goes through all the possible shapes and lists them in order from best to worst fit based on residuals.
In some cases, when the standard Least Squares method with orthogonal projection does not work, best fit for Line, Parabola, Polynomial and Trigonometric functions can be calculated with SVD.
Links to four other free apps by same developers are included in the app:
1. “Matrix Solver Step by Step” Linear Algebra Visual Guide.
2. “Polynomials and Linear Systems” Equation Solver.
3. “GraphMath” Graphing Calculator.
4. “Vectors and Planes” (and Spheres and Ellipsoids) 3D Geometry Guide.
Developers hope to get feedback from users at graphmath@aol.com.
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PP+ Force Vector Addition VS.
Least Squares Curve Fit
gennaio 12, 2025