Periodic Modeling

Explore period and units, parameters in context, model limits.

Lesson 5 of 53 parts Practice Flashcards

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Period and Units

Objective: Explain period and units and use it to solve or interpret a problem.

A periodic model repeats after a stated interval; input units such as hours must match the period. A cycle observed once does not guarantee perpetual repetition. A number alone cannot tell whether a cycle is hours or days.

Worked examples

Try itPeriodic Modeling — practice 1.1: A periodic model repeats every 5 hours. If its value at t=1 is 4, what is its value at t=6?Show answer

Step 1: The two times differ by 5 hours. Step 2: That is exactly one full period. Step 3: The output repeats and equals 4.

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Period and Units

Objective: Explain period and units and use it to solve or interpret a problem.

Worked examples

Try itPeriodic Modeling — practice 1.1: A periodic model repeats every 5 hours. If its value at t=1 is 4, what is its value at t=6?Show answer

Step 1: The two times differ by 5 hours. Step 2: That is exactly one full period. Step 3: The output repeats and equals 4.

Parameters in Context

Objective: Explain parameters in context and use it to solve or interpret a problem.

Amplitude measures deviation from a midline, while phase locates a feature in time. Explain how sampling and noise influence a fitted model. No, many periodic curves pass through one point.

Worked examples

Try itPeriodic Modeling — practice 2.1: For y=3sin(8x)+5, find amplitude.Show answer

Step 1: Amplitude is the absolute value of sine coefficient. Step 2: |3|=3. Step 3: The amplitude is 3.

Model Limits

Objective: Explain model limits and use it to solve or interpret a problem.

A sine model is useful only while repetition is plausible; compare new observations and residuals, and avoid assuming a natural cycle is perfectly regular. Systematic misses can reveal an inadequate model.

Worked examples

Try itPeriodic Modeling — practice 3.1: A periodic model repeats every 11 hours. If its value at t=1 is 6, what is its value at t=12?Show answer

Step 1: The two times differ by 11 hours. Step 2: That is exactly one full period. Step 3: The output repeats and equals 6.

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