Math 1060

Mass Spring Project

In trigonometry we explored several ways to apply mathematics to shapes.  This is one of the areas of math that can be visually seen in real life.  During one of our class discussions we related our studies to our future and current careers, and found that an understanding of trigonometry would prove useful—if not necessary—for a wide breadth of topics.

Our signature project was on the motion of a spring.  This project covered multiple topics from our course this semester.  The first application of this that I thought of was a swing.  I remember, as an elementary student, always trying to reach the highest height.  It was always in the back of my mind that I could fly over the top of the swing set, so I held myself back a bit.  Another reason for this was because there was the inevitable fly from the moving swing and land standing (if you were a true dare-devil) to end playtime—the things you hope your own children never think to do.  If I had an understanding of velocity and mass springs systems, I would have been able to calculate the velocity at which you could push yourself over the bar.

Another mystery to me at this age was the tuning fork.  I remember leaving choir practice and grabbing a silverware fork and knife from the drawer when I got home, and banging them together.  I never could produce the equivalent of the “A” above the middle “C”; just a clanging sound.  If I applied mass springs systems to these household utensils, I would have quickly noticed that there were twice as many tines and the length was not long enough to produce the correct frequency of sound waves.

Fast forward to present-day.  I frequently use microphones at work.  The ability to pick up sound waves (frequencies) and submit these signals to an amplifier for the sound to be heard somewhere else is explained by mass springs systems, as well.  Furthermore, interference or feedback is readily explained in the same fashion.

Trigonometry has never been my favorite subject of mathematics.  I always preferred equations to pictures and real-life applications.  However, after taking this class I saw the usefulness of them.  I was challenged, at first, by the examples of flight bearings in the homework, test, and quizzes—especially since I never knew that bearing was measured from the North.  When I took the time to understand the steps and why, the law of sines and cosines were no longer equations to memorize and regurgitate, but I could formulate a picture in my mind of why it would be true of those values.  This also helped me to catch errors because I could ask myself if that answer seemed correct.