This resource is a Java applet-based module relating to the simple harmonic motion produced by a block on a frictionless spring. It features a rich array of tools: motion graphs, energy graphs, vector components, reference circle, zoom toggle, and a data box that displays amplitude, angular frequency, displacement from equilibrium, phase angle, velocity, and acceleration of the oscillating block. Users control the spring constant, mass of the block, and amplitude of the oscillation. A comprehensive help section provides detailed directions and lesson ideas for instructors.

This simulation is part of a larger collection of physics resources sponsored by the MAP project (Modular Approach to Physics).

Editor's Note:This is one of the best resources we've found for exploring simple harmonic motion and its sinusoidal nature. It can be adapted for course levels ranging from 9th grade physical science to calculus-based college physics courses. It covers kinematic properties, the dynamics of SHM, and explicit diagrams on sine/cosine functions illustrated through the unit circle. It will help learners understand that SHM is a motion identical to the projection of a uniform circular motion onto a straight line (Math Common Core F-TF.2, F-TF4, High School Trigonometric Functions)

Hooke's Law, MAP, SHM, angular frequency, conservation of energy, interactive simulation, lesson plan, mass and spring, oscillating, oscillator, radian, simple harmonic motion, simulation, spring, springs, unit circle

Record Cloner:

Metadata instance created May 22, 2008
by Christopher Allen

9-12: 2A/H1. Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world.

4. The Physical Setting

4E. Energy Transformations

9-12: 4E/H1. Although the various forms of energy appear very different, each can be measured in a way that makes it possible to keep track of how much of one form is converted into another. Whenever the amount of energy in one place diminishes, the amount in other places or forms increases by the same amount.

4F. Motion

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.

11. Common Themes

11B. Models

6-8: 11B/M2. Mathematical models can be displayed on a computer and then modified to see what happens.

6-8: 11B/M4. Simulations are often useful in modeling events and processes.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

Functions (8)

Use functions to model relationships between quantities. (8)

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

High School — Algebra (9-12)

Seeing Structure in Expressions (9-12)

A-SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^{?}

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.^{?}

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Building Functions (9-12)

F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Trigonometric Functions (9-12)

F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

F-TF.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.^{?}

Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12

Craft and Structure (6-12)

RST.11-12.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11—12 texts and topics.

Integration of Knowledge and Ideas (6-12)

RST.11-12.9 Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible.

Range of Reading and Level of Text Complexity (6-12)

RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11—CCR text complexity band independently and proficiently.

<a href="https://www.compadre.org/precollege/items/detail.cfm?ID=7222">University of Calgary. Modular Approach to Physics: Simple Harmonic Motion - Weighted Spring. Calgary: University of Calgary, March 30, 2007.</a>

Modular Approach to Physics: Simple Harmonic Motion - Weighted Spring. (2007, March 30). Retrieved March 21, 2023, from University of Calgary: http://canu.ucalgary.ca/map/content/shm/springEnergy/simulate/page2.html

University of Calgary. Modular Approach to Physics: Simple Harmonic Motion - Weighted Spring. Calgary: University of Calgary, March 30, 2007. http://canu.ucalgary.ca/map/content/shm/springEnergy/simulate/page2.html (accessed 21 March 2023).

Modular Approach to Physics: Simple Harmonic Motion - Weighted Spring. Calgary: University of Calgary, 2001. 30 Mar. 2007. 21 Mar. 2023 <http://canu.ucalgary.ca/map/content/shm/springEnergy/simulate/page2.html>.

%T Modular Approach to Physics: Simple Harmonic Motion - Weighted Spring %D March 30, 2007 %I University of Calgary %C Calgary %U http://canu.ucalgary.ca/map/content/shm/springEnergy/simulate/page2.html %O application/java

%0 Electronic Source %D March 30, 2007 %T Modular Approach to Physics: Simple Harmonic Motion - Weighted Spring %I University of Calgary %V 2023 %N 21 March 2023 %8 March 30, 2007 %9 application/java %U http://canu.ucalgary.ca/map/content/shm/springEnergy/simulate/page2.html

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