Modeling Oscillating Systems: Physics Component Standards Addressed |

**CONTENT STANDARD A: As a result of activities in grades 9-12,
all students should develop **

- Abilities necessary to do scientific inquiry
- Understandings about scientific inquiry

** Motions and Forces **

- Objects change their motion only when a net force is applied. Laws of motion are used to calculate precisely the effects of forces on the motion of objects. The magnitude of the change in motion can be calculated using the relationship F=ma, which is independent of the nature of the force. Whenever one object exerts force on another, a force equal in magnitude and opposite in direction is exerted on the first object.

By the end of the 12th grade, students should know that

- Content Standards - Physical Science
- The change in motion of an object is proportional to the applied force and inversely proportional to the mass.

- Common Themes
- Systems
- A system usually has some properties that are different from those of its parts, but appear because of the interaction of those parts.
- The successful operation of a designed system usually involves feedback. The feedback of output from some parts of a system to input of other parts can be used to encourage what is going on in a system, discourage it, or reduce its discrepancy from some desired value. The stability of a system can be greater when it includes appropriate feedback mechanisms. Even in some very simple systems, it may not always be possible to predict accurately the result of changing some part or connection.

- Models
- The basic idea of mathematical modeling is to find a mathematical relationship that behaves in the same ways as the objects or processes under investigation. A mathematical model may give insight about how something really works or may fit observations very well without any intuitive meaning.
- Computers have greatly improved the power and use of mathematical models by performing computations that are very long, very complicated, or repetitive. Therefore computers can show the consequences of applying complex rules or of changing the rules. The graphic capabilities of computers make them useful in the design and testing of devices and structures and in the simulation of complicated processes.
- The usefulness of a model can be tested by comparing its predictions to actual observations in the real world. But a close match does not necessarily mean that the model is the only "true" model or the only one that would work.

- Constancy and Change
- A system in equilibrium may return to the same state of equilibrium if the disturbances it experiences are small. But large disturbances may cause it to escape that equilibrium and eventually settle into some other state of equilibrium.
- Graphs and equations are useful (and often equivalent) ways for depicting and analyzing patterns of change.
- In many physical, biological, and social systems, changes in one direction tend to produce opposing (but somewhat delayed) influences, leading to repetitive cycles of behavior.

- Systems

- Multiple indicators under Core Goal 1 - Skills and Processes
- Core Goal 5 - Physics
The student will demonstrate the ability to use scientific skills and processes (Core Learning Goal 1) to explain and predict the outcome of certain interactions which occur between matter and energy.

- Expectation
5.1 - The student will know and apply the laws of mechanics to explain the
behavior of the physical world.
- Indicator
5.1.1 - The student will use analytical techniques appropriate to the study of
physics.
- AT LEAST: symbolically representing vector quantities, using signs to represent directions, selecting and using appropriate equipment for measuring and investigating, using appropriate units and applying dimensional analysis, manipulating equations

- Indicator 5.1.2 - The student will use
algebraic and geometric concepts to describe an object's motion.
- AT LEAST: direction, position, distance/displacement, speed/velocity, motion with a constant acceleration, one and two dimensional motion, frames of reference

- Indicator 5.1.3 - The student will analyze
and explain how changes in an object's motion are described by Newton's Laws.
- AT LEAST: balanced/unbalanced forces, inertia, acceleration, force, and mass, action/reaction

- Indicator
5.1.1 - The student will use analytical techniques appropriate to the study of
physics.
- Expectation 5.7 - The student will show that connections
exist both within the various fields of science and among science and other
disciplines including mathematics, social studies, language arts, fine arts,
and technology.
- Indicator 5.7.2 - The student will recognize the important role that mathematics serves when solving problems in physics.

- Expectation
5.1 - The student will know and apply the laws of mechanics to explain the
behavior of the physical world.