Algebra and Trigonometry damped oscillator, ball arc

White board images from a damped oscillator consisting of a spring with a weight on the bottom. Equations are on the board and require an initial amplitude, an exponential decay rate coefficient, and a sine wave function.

Above are some undamped calculations on the spring

The spring oscillation was allowed to decay

Ball arc calculations. A radar gun was used to determine the velocity of the ball. A stopwatch and GPS determined the horizontal velocity. I estimated theta with a protractor. I forgot to have someone take photos of the set-up on the front lawn. The team also included a pitcher and catcher. Both high and low arc balls were thrown. The ball was a foursquare ball.

Raw data for for throws:
Theta estimated at 75 degrees.
Radar gun: 29 kph
Time: 2 seconds
Distance: 13 meters

Theta estimated at 80 degrees.
Radar gun: 29 kph (again)
Time: 1.75 seconds
Distance: 13 meters

Theta estimated at 35 degrees.
Radar gun: 39 kph
Time: 1.3 seconds
Distance: 13 meters

Theta estimated at 30 degrees.
Radar gun: 45 kph
Time: 0.95 seconds
Distance: 13 meters

Note that the system is overspecified and that the numbers are not internally consistent.
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