A Physics student recorded the movement of a spring apparatus for 10 seconds. She displaced the spring 5 inches up (positive displacement) from its resting (midline=0) position and released it at the instant (t=0) she began recording. The spring moved down (negative displacement) and back up several times. It took 10 seconds total to bounce from top to bottom and back up to its starting, top position 20 times (20 complete cycles) during the experiment. The total distance from bottom to top was 10 inches. Write and graph the function that represents the pendulum’s displacement as a function of time.

A-Given that the experiment started when the spring was at its maximum positive displacement position (at t = 0) what trig function would be the most obvious to use for the model? Also, what is the amplitude and period of the function? (Include units on your answers!)

B-Write an equation that models the motion of the pendulum where f(x) is the displacement of the spring in inches and ‘x’ (or t) is time in seconds. (Assume the mid-line is y=0.)

C-Graph at least two complete cycles of the function using your equation from B above. You may make a hand drawn sketch, a hand drawn graph using your own graph paper, or you may use Desmos or other graphing software or calculator to make the graph. Be sure your graph has clearly labeled axes so that the amplitude and period of your function can be easily seen!