Wednesday, February 5, 2014

Sinusoid Lab Activities

Nothing helps students get a good handle on mathematical concepts than lab activities that addresses the subtleties and true meaning of the underlying components that accompany such concepts.

Following is a description of a set of lab activities that deal with the sinusoid and its usefulness in trig and in many real life situations that are periodic in nature. 

Day 1: Students were handed a plot, that I obtained in an experiment I conducted as a test run, to model it themselves using the sinusoid (transformed basic sine function) involving the h & k form. First the students had to work alone, then with a partner, and then in a group to assist one another with the modeling process.

Day 2: Students were handed a data set to enter the first two columns in their respective TI calculators and as a class we worked together to plot the data, model them ourselves as a class, and then the class was broken into three groups whose assignment was to carry out the same process but for columns one and three, one and four, and one and five respectively. The rest of the work consisted of students competing for the best fit equation generated by hand and the group member with the equation that fit the best than her/his group peers will be treated to delicious sweets. No TI sine regression was allowed.

Day 3: Students's regression equations were pitted against one another for each group and the best fit equations were identified and the equations owners were treated to double sweets while the rest of the folks (who did attempt a decent fit of some sort) got single sweets. Afterwards, the sine regression functionality in the TI calculator was introduced and now the students were ready to carry out the lab activities themselves. The setups, the procedures, and all technology matters were introduced. Following, are the pictures of the various setups.

First Setup: The pendulum is facing the motion detector that is resting on a make-shift bubble gum box. The students in this group will alternate in collecting data onto their respective laptops. From the camera perspective, another group is going to use LoggerPro's video capture of the same motions of the pendulum (see picture below.)
Second Setup: The pendulum motion is recorded laterally by the members of another group using LoggerPro's video capture of the same motions of the pendulum that the first group is recording. The idea here is to allow for cross referencing and checking of the various group members' data and results.
Third Setup: An iPad is hanging as a bob from a spring that is attached to a force probe. The oscillatory motion is recorded in two ways, the acceleration of the iPad using SPARKvue app from within the iPad itself (see next pictures) and force using Vernier's dual force probe whose results are fed directly to LoggerPro of the students' laptops. Once again the idea here is to allow for cross referencing and checking of the various group members' data and results using two different means of gathering data related to the same motion.

Day 4: Students did the actual lab; the scene was lively, the graphs were gems (an example is shown below), and the thinking and enthusiasm were Coolism! 

The graph of the oscillatory motion of the iPad shows three parts, the hand picking the iPad to start the recording of the motion, the oscillation, and final the hand picking the iPad again to stop recording the motion.

Once the data collection process was completed and every student obtained her/his data and graphs on their respective laptops, the task of switching LoggerPro's form to the form. This part ended up being the homework that was due next day; every student had to complete the form change and make the predictions requested in parts B, C, & D listed in the lab sheet.

Day 5: Students showed their form changes and their predictions, compared their respective constants, and then discussed their predictions and how they would be checked empirically.

As a whole the activity was not just fun but also led to many insights. The experiment is still in progress in that a followup lab that will make the oscillations dampened shall ensue when exponential functions come into the picture.

Thank you for reading the post and please provide some feedback, suggestions, or variations you deem worth consideration. 

Thank you and take great care! :-) 

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