My name is Carlos and I am a student at Salt Lake Community College.  This is a post about a Trigonometry project my class was assigned.  The assignment states as follows:

Give some examples of mass-spring systems important in every day life.  Describe why it would be important to understand the amplitude, period, and frequency of these systems.  Did this project change the way you think about how trigonometry can be applied to the real world?  State what ideas changed and why.  If this project did not change the way you think, write how this project gave further evidence to support your existing opinion of applying trigonometry. Be Specific.

Give some examples of mass-spring systems important in every day life: Although mass-spring systems are most likely not directly used in everyday life, analyzing problems using trigonometry is used more often.  If, for example, you are interested in woodworking, you might use trigonometry to find the length of sides or angles in which to cut wood at.  If you like making computer based gravity simulators (games), you might use vectors and vector logic to keep track of velocity, acceleration, etc.

Describe why it would be important to understand the amplitude, period, and frequency of these systems:  It is important to understand these concepts because they will give you a general understanding that functions can be more easily understood than what your first impression of these systems might have been.  It is also important to understand these things because you can come up with some awesome systems using differing amplitude, period, and frequency applied to animation.  Take, for example, animating a jelly blob.  The “jiggliness” could be implemented programatically as a function of sin.  The amplitude would describe how strong the “jiggle” is.  The frequency would be how many “jiggles” this blob might have per unit of time.  The period would describe one cycle of the frequency and could be used to visualize how often the blob will “jiggle.”  These functions could be used to describe anything with a repeating wave.

Did this project change the way you think about how trigonometry can be applied to the real world?  State what ideas changed and why:  In short, yes.  In a longer form, yes it did.  Understanding these systems made me realize that they could be applied to things other than position.  For instance, one could use these trigonometric functions to describe how something seems to get gradually bigger and smaller.  The scale factor could be described as the y position of a sin function and the x axis would be time.  As time goes forward, the scale would gradually get bigger and smaller depending on what the amplitude, period, phase shift, and y-shift might be.  This could be applied to animating a number of things which gradually get bigger and smaller.  If one is animating a sun in a program, you could animate the sun to grow a little bigger and smaller every frame to make it look like it’s more alive than just a simple solid sphere.

The last part of the question does not apply since this project did change the way I thought about the mass-spring model.  The following is my mass-spring model assignment.  To download it in PDF format, click here.

 

ImageImageImageImageImage