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.
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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