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Trigonometric Graphs
Word problem involving a sine or cosine function: Problem type 1
Jameson
Español
An object moves in simple harmonic motion with amplitude 
8m and period 2 minutes. At time 
t=0 minutes, its displacement 
d from rest is 
-8m, and initially it moves in a positive direction.
Give the equation modeling the displacement 
d as a function of time 
t.

d=

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2:16 PM

4//22//2024

Import favorites\newlineMVNU Students Ho...\newlineA\newlineALEKS - Jameson C...\newlineTrigonometric Graphs\newlineWord problem involving a sine or cosine function: Problem type 11\newlineJameson\newlineEspañol\newlineAn object moves in simple harmonic motion with amplitude 8 m 8 \mathrm{~m} and period 22 minutes. At time t=0 t=0 minutes, its displacement d d from rest is 8 m -8 \mathrm{~m} , and initially it moves in a positive direction.\newlineGive the equation modeling the displacement d d as a function of time t t .\newlined= d= \newline \square \newline \square \newlineExplanation\newlineCheck\newline(C) 20242024 McGraw Hill LLC. All Rights Reserved.\newlineTerms of Use\newlinePrivacy Center\newlineAccessibility\newlineType here to search\newline59F 59^{\circ} \mathrm{F} \newline(11))\newline22:1616 PM\newline4/22/2024 4 / 22 / 2024

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Q. Import favorites\newlineMVNU Students Ho...\newlineA\newlineALEKS - Jameson C...\newlineTrigonometric Graphs\newlineWord problem involving a sine or cosine function: Problem type 11\newlineJameson\newlineEspañol\newlineAn object moves in simple harmonic motion with amplitude 8 m 8 \mathrm{~m} and period 22 minutes. At time t=0 t=0 minutes, its displacement d d from rest is 8 m -8 \mathrm{~m} , and initially it moves in a positive direction.\newlineGive the equation modeling the displacement d d as a function of time t t .\newlined= d= \newline \square \newline \square \newlineExplanation\newlineCheck\newline(C) 20242024 McGraw Hill LLC. All Rights Reserved.\newlineTerms of Use\newlinePrivacy Center\newlineAccessibility\newlineType here to search\newline59F 59^{\circ} \mathrm{F} \newline(11))\newline22:1616 PM\newline4/22/2024 4 / 22 / 2024
  1. Amplitude Explanation: The amplitude of the motion is 8m8\,\text{m}, which means the maximum displacement from the rest position is 8m8\,\text{m}.
  2. Period Explanation: The period of the motion is 22 minutes, which is the time it takes for one complete cycle of the motion.
  3. Cosine Function Selection: Since the object starts at 8m-8\,\text{m} and moves in a positive direction, we use the cosine function, which starts at its maximum value and decreases first.
  4. Equation Form: The general form of the equation for simple harmonic motion is d(t)=Acos(2πPeriodt+Phase Shift)d(t) = A \cdot \cos\left(\frac{2\pi}{\text{Period}} \cdot t + \text{Phase Shift}\right), where AA is the amplitude.
  5. Equation Application: We plug in the amplitude (8m8\,\text{m}) and the period (2minutes2\,\text{minutes}) into the equation. Since the period is in minutes, we need to convert it to seconds by multiplying by 6060, as the standard unit for time in these equations is seconds.\newlined(t)=8cos(2π260t+Phase Shift)d(t) = 8 \cdot \cos\left(\frac{2\pi}{2 \cdot 60} \cdot t + \text{Phase Shift}\right)

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