November 11, 2016

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).

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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.

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.

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

Model with mathematics.

Use functions to model relationships between quantities.

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.

Interpret the structure of expressions

Interpret expressions that represent a quantity in terms of its context ?

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret functions that arise in applications in terms of the context

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.?

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.?

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.?

Analyze functions using different representations

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

Build new functions from existing functions

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.

Extend the domain of trigonometric functions using the unit circle

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

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.

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

Model periodic phenomena with trigonometric functions

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.?