A scientist recorded the movement of a pendulum for 10 s. 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 took 4 s to swing to the right and the left and then return to its resting position. The pendulum’s furthest distance to either side was 6 in. Graph the function that represents the pendulum’s displacement as a function of time.

(A) Write an equation to represent the displacement of the pendulum as a function of time.

(B) Graph the function.

oscar.a1551 Feb 20, 2019

#1**+4 **

(1) This is just the basic sine graph shifted down 2 units

Here is the graph : https://www.desmos.com/calculator/6ppigmmzbe

(2) This is the basic cosine graph with a period of pi shifted up 1 unit

Here is the graph : https://www.desmos.com/calculator/okxkxbmj5d

(3) A scientist recorded the movement of a pendulum for 10 s. 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 took 4 s to swing to the right and the left and then return to its resting position. The pendulum’s furthest distance to either side was 6 in. Graph the function that represents the pendulum’s displacement as a function of time.

The form is

y = Asin (Bx)

A = the amplitude = 6

The period is 4 seconds

B = 2pi / period = 2pi / 4 = pi/2

The function is

y = 6sin ( pi * t / 2 )

Here is the graph : https://www.desmos.com/calculator/u7pe5zrrft

CPhill Feb 20, 2019