TEACHER NOTES

ISSUES RELATED TO THE PROBLEM

This problem requires to estimate the values of a, b, c, and d in the model h(t) = a sin b(t + c) + d where t is time in hours after midnight and h(t) is the height of the water in Oakland Bay.

The approach is to eyeball estimate, not truly fit, and to compare the estimate model with the data and use the model to predict height and rate of change of height. With regard to the latter rate, one can take the formal derivative or use a difference quotient form of the derivative over a small interval to approximate the instantaneous change at time t.

The problem is not much different or much more difficult than the standard simple harmonic motion problem. It does have the nice feature that the information is given to the students in the form of a table. This gives a nice introduction into the topics of data analysis and curve fitting.

Prerequisites

Students should have seen the basic function h(t) = a sin b(t + c) + d. They should have seen graphs and understand the significance of each of the terms a, b, c, and d.

Time allotment - time management

This activity can be done in one half hour or so with appropriate technology during class time.

Expectations

Future payoffs

Extensions

References and Sources