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Perplex
  • Dashboard
Topics
Exponents & LogarithmsRounding & ErrorSequences & SeriesFinancial MathematicsMatricesComplex Numbers
Cartesian plane & linesFunction TheoryModellingTransformations & asymptotes
2D & 3D GeometryVoronoi DiagramsTrig equations & identitiesVectorsGraph Theory
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random VariablesInference & Hypotheses
DifferentiationIntegrationDifferential Equations
Paper 3
Plus
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Perplex

Modelling (Lesson 5/10)

Sinuisoidal Models

1 / 10

Discussion

Robert swings a pendulum and plots its height ​h, in centimeters, versus time ​t​ in seconds:

Describe how a model for the height of the pendulum as a function of time would look.

Solution:

The graph of height versus time would be a single, smooth curve passing through the given points and then repeating its shape over and over. Visually, starting at the initial high point, the curve would sweep down to the low point, then rise back up to a high point, fall again, and so on in a regular, wave‐like pattern.


There are no sharp corners or breaks—just a continuous “up–down–up–down” motion of fixed size and time.


To capture that periodic, oscillating behavior one often uses functions that rise and fall smoothly—most commonly sine or cosine curves—to model the height of a pendulum over time.

1 free

Modelling (Lesson 5/10)

Sinuisoidal Models

1 / 10

Discussion

Robert swings a pendulum and plots its height ​h, in centimeters, versus time ​t​ in seconds:

Describe how a model for the height of the pendulum as a function of time would look.

Solution:

The graph of height versus time would be a single, smooth curve passing through the given points and then repeating its shape over and over. Visually, starting at the initial high point, the curve would sweep down to the low point, then rise back up to a high point, fall again, and so on in a regular, wave‐like pattern.


There are no sharp corners or breaks—just a continuous “up–down–up–down” motion of fixed size and time.


To capture that periodic, oscillating behavior one often uses functions that rise and fall smoothly—most commonly sine or cosine curves—to model the height of a pendulum over time.

1 free