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A scientist recorded the movement of a pendulum for 15s. The scientist began recording when the pendulum was at its resting position. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum’s furthest distance to either side was 7 in. The pendulum took 8 s to swing to the right and the left and then return to its resting position. (a) Write an equation to represent the displacement of the pendulum as a function of time. Show all work and explain how you determined each parameter in the equation. (4 points)

 Feb 17, 2022
 #1
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We can model this with the sine function

 

We have this form

 

y  =  Asin (Bx)

 

y = the displacement   at any time, x

A = the amplitude =  7 in

x= time in sec

The period =  8s

B =   2pi / 8  =  pi/4

 

The function  is     y =  7sin [ (pi / 4)  x ] 

 

Here's a graph  :   https://www.desmos.com/calculator/urhpnycwzv

 

 

cool cool cool

 Feb 17, 2022
 #2
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Thank you!!!

Guest Feb 17, 2022

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