Import favoritesMVNU Students Ho...AALEKS - Jameson C...Trigonometric GraphsWord problem involving a sine or cosine function: Problem type 1JamesonEspañolAn 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=□□ExplanationCheck(C) 2024 McGraw Hill LLC. All Rights Reserved.Terms of UsePrivacy CenterAccessibilityType here to search59∘F(1))2:16 PM4/22/2024
Q. Import favoritesMVNU Students Ho...AALEKS - Jameson C...Trigonometric GraphsWord problem involving a sine or cosine function: Problem type 1JamesonEspañolAn 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=□□ExplanationCheck(C) 2024 McGraw Hill LLC. All Rights Reserved.Terms of UsePrivacy CenterAccessibilityType here to search59∘F(1))2:16 PM4/22/2024
Amplitude Explanation: The amplitude of the motion is 8m, which means the maximum displacement from the rest position is 8m.
Period Explanation: The period of the motion is 2 minutes, which is the time it takes for one complete cycle of the motion.
Cosine Function Selection: Since the object starts at −8m and moves in a positive direction, we use the cosine function, which starts at its maximum value and decreases first.
Equation Form: The general form of the equation for simple harmonic motion is d(t)=A⋅cos(Period2π⋅t+Phase Shift), where A is the amplitude.
Equation Application: We plug in the amplitude (8m) and the period (2minutes) into the equation. Since the period is in minutes, we need to convert it to seconds by multiplying by 60, as the standard unit for time in these equations is seconds.d(t)=8⋅cos(2⋅602π⋅t+Phase Shift)
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