An object moves in simple harmonic motion with period 8 minutes and amplitude 16 m. At time t = 0 minutes, its displacement d from rest is 0 m, and initially it moves in a positive direction. Give the equation modeling the displacement d as a function of time f.

Question
Modeling
asked 2021-01-27
An object moves in simple harmonic motion with period 8 minutes and amplitude 16 m. At time \(t = 0\) minutes, its displacement d from rest is 0 m, and initially it moves in a positive direction. Give the equation modeling the displacement d as a function of time f.

Answers (1)

2021-01-28
Step 1 Equation modeling the diplacement d as function of time = A sin wt where A = amplitude and time period = 2pi//w Step 2 \(A = amplitude = 16 m\) \(Period = 8 minutes = 8 \times 60 = 480 seconds = 2\pi/w\) Hence, \(w = 2pi/480 = \pi/240\) Step 3 Hence, \(d = 16sin(\pi t/240)\)
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