# 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
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.

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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