# 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.

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.
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Jayden-James Duffy

Step 1 Equation modeling the diplacement d as function of time = A sin wt where A = amplitude and time period $=\frac{2\pi }{w}$

Step 2 $A=amplitude=16m$

Hence, $w=\frac{2\pi }{480}=\frac{\pi }{240}$

Step 3 Hence, $d=16\mathrm{sin}\left(\frac{\pi t}{240}\right)$