50 POINTS FOR THE CORRECT ANSWER A scientist recorded the movement of a pendulum for 12 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 7 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

Step-by-step explanation:

angular frequency

ω = 2π/ T = 2π/4 = π/2 rad/s

A = 7 inch

Starts at rest (maximum swing, |A| = 7) so cosine function is easiest

x = -7cos(πt/2)

The amplitude is 6.

We can use the sine here. I'm assuming that the period is 4 seconds. so each second is

So, we have this function

NOTE: See picture attached.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

4.08%

step-by-step explanation: