This experiment can be used in a general education mathematics class, a calculus class, or a differential equations
class when studying periodic functions, exponential functions, or harmonic motion. For this experiment, we set up
a damped mass-spring system by placing the mass into a clear container filled with water. The water causes the
system to become damped. We then set this damped system into motion, recorded a video, and imported its frames
into TEMATH. We used TEMATH's Point tool to mark the position of the mass in each frame. The y-coordinate of
the positions were placed into a table and plotted as a function of time resulting in a pattern of the exponentially
damped sinusoid
y = a e^(-kt) sin((2 /T) (t - b)) - c
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where a is the amplitude, k is the damping coefficient, T is the period, b is the horizontal
shift, and c is the vertical shift. In this experiment, students must model both an exponential function and a
sinusoid. This is an excellent model to use with students when studying periodic functions or exponential functions.
