A Physics student recorded the movement of a swinging pendulum for 10 s (seconds). The student began recording when the pendulum was at its resting (vertical) position but moving to the right. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 2 s to swing to the right and the left and then return to its resting position. The pendulum’s furthest distance to either side of vertical was 3 in. Graph the function that represents the pendulum’s displacement as a function of time. Answer each of the following questions for five points each. 15 points total.
Given that the experiment started when the swinging pendulum was at its vertical position (time = 0) what trig function would be the most obvious to use for the model? Also, what is the amplitude and period of the function?
Using your answers from A, B, and C above, write an equation that models the motion of the pendulum.
Graph at least two complete cycles of the function using your equation from D above. You may use Desmos or other graphing software to make the graph. Be sure your graph has clearly labeled axes so that the amplitude and period of your function can be seen!
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I'm assuming that when the problem says " 2s to the right and left and the return to its original position " that the total period is 4 seconds.....
So.... the period is 4 seconds ....
The amplitude is 3
The sine fuction seeks to model this best
In the form
y = Asin (Bx)
A = amplitude = 3
To find B, we need to solve this
B = 2pi / period = 2pi/ 4 = pi/2
So....our function becomes
y = 3sin ( (pi/2) * x )
Here's the graph ....two periods are shown :
https://www.desmos.com/calculator/skrl7kbslk
