As a third-year Biomedical Engineering student at the University of Guelph, learning throughout this pandemic has been especially difficult, but why? It’s all the same materials. The same teaching style. I can even choose my learning environment and mitigate distractions.

For me, the biggest thing that has been missing throughout this pandemic has been experimentation, but more specifically, labs that push students to apply their knowledge to their own observations or to the world around them. During this pandemic, I took a course called Biomechanics as an extracurricular. Without a doubt in my mind, this course ignited my passion for practical application. Students were required to observe, collect, and write three different labs, all centered around the biomechanics of crutch walking. After learning to use a goniometer, force plate, EMG sensors, and 3D modelling software, students then created their own biomechanics experiment.

This is where the real learning begins.

What does this have anything to do with harmonics or even Capstone, you may ask? The point I am trying to make is that you can throw complicated laws and theorems a student’s way. However, they won’t understand it until they begin to connect these laws to the world around them. Every student has asked, “When will I ever use this?” but rarely do you ever find a student who seeks the question “How does this affect the world around me?” As such, I wanted to pose a simple question that pushes students to connect their knowledge outside the classroom.

What are some examples of harmonic motion in your daily life?

This question is really nothing special, but it can be easily observed and analyzed with little to no equipment. For this example, I used PASCO’s Capstone Software going frame by frame to analyze the motion of various objects and graphing the vertical position (meters) versus time (seconds).

The first example of harmonic motion was the spinning of a bicycle wheel, which was suspended to have no contact with other objects. Three different examples of periodic rotation were observed using the Capstone software and a bright green piece of tape.

The green line represents a graph that has no brakes applied, the blue line represents a system with light braking pressure, and the red line represents a system with full braking.

From the data collected, it was observed that as the brake pressure is increased, the period of the oscillator decreased. This trend is essential for students to understand as it raises the question of braking distance and the effects of friction on a periodic oscillator.

The next example of harmonic motion was car suspension. The system represents a driven harmonic oscillator as most car suspensions will be critically damped or have some sort of dampening. For this experiment, I highly recommend filming the oscillation in real-time with an additional light source. The top of the spring was tracked throughout the cycle and plotted on a vertical position vs. time graph.

The blue line represents the effect of the applied force on the vertical position (meters) of the spring vs. time (seconds).

As a final example of harmonic motion, the E-String of a guitar was filmed using the slow-motion setting on a phone, shooting at about 960 fps. String harmonics are incredibly difficult to capture, and for a more accurate measurement, I highly recommend the use of a slow-motion camera. As an alternate example of harmonic motion, I recommend a swing, metronome, or any pendulum clock.

This graph represents the vertical position (centimeters) of the guitar string vs. time (s).

Laboratory experimentation is usually very equipment-heavy, which prevents students from observing the effects of the laws and theorems on a day-to-day basis. The difficulty of tracking time, position, or other factors removes focus from the real learning and can often times impede a student’s understanding. The best way to foster a student’s understanding is through their own curiosity.

It’s that time of year again. Chemistry teachers everywhere are dusting of their pun-ny jokes and creating mole-themed, activities and treats to celebrate National Mole Day in commemoration of Avogadro’s number (6.02 x 10²³). Mole Day is celebrated starting at 6:02 am on October 23rd. How will we be celebrating? With chips and Guaca-mole, of course!

As we introduce the topic to students we typically start with something they already know. A mole, like a dozen, is a way of counting things. It just so happens that a mole is a really large number. While 1 dozen equals 12, 1 mole equals 6.02 x 10²³. This number has to be very large because the particles that we deal with in chemistry happen to be very, very small (or sm-ole… the bad jokes keep on coming).

To give students a mole-ecular perspective of those tiny particles, you can use a modeling kit.

At this point in the year it is important for students to understand the basics of chemical formulas. The model kit gives them something to see and touch as they learn that subscripts in a formula represent the number of atoms that are bonded in the compound.

In addition to formulas, the model kit can be useful in calculating molar mass. Since each different colored atom represents a different molar mass, students can just take their model and add up all the masses of all the atoms that they see! In the case of water, the oxygen is 16 grams per mole and each hydrogen is 1 gram per mole. In total, there are 18 grams for every one mole of water molecules.

So how do chemists relate these tiny particles to something that they can measure, like grams? Moles to the rescue! Avogadro’s number (the number of particles in one mole) and molar mass (the amount of grams in one mole) both meet in the middle at … moles.

Moles are central to counting particles in chemistry. Using Avogadro’s number and the molar mass of water, we know that there are 6.02 x 10²³ molecules in graduated cylinder that contains 18 grams of water.

Model kits can be great tools in helping students visually and kinesthetically learn about chemical formulas. They become actively engaged in the learning process as they discover the meaning and value of subscripts, molar masses and, of course, Avogadro’s number. And as students gain a better understanding of these concepts the real fun begins— they start to really understand your science humor! “Oh no! I’ve spilled water on my book!”

Happy Mole Day!

Students use conductometric titration and gravimetry to determine how much calcium carbonate is in a sample of tap water.

This lab is an introduction to methodological comparisons. Percent error is calculated for both gravimetry and titration. Samples of tap water from various locales are concentrated and analyzed for calcium content.

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Student Files

• 03_ACI_How_Hard_Is_Your_Tap_Water_S.docx
• 03_ACI_How_Hard_Is_Your_Tap_Water_S.pdf

Standards Correlations

• IB Topics
  • 1.4
• AP Topics
  • SPQ-1.A; SPQ-2.A; TRA-1.C; SPQ-3.C; SPQ-4.A

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