Give the equation modeling the displacement

Question

An object moves in simple harmonic motion with amplitude 8m and period 1 minute. 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

*provide explanation as well*

Answer 1

ω = 2π/P; in this case, 2π/1 = 2π

Since we start off at the minimum, the easiest function to use will be -cos, as cos has a maximum at 0.

Thus, our equation will be d = -8 cos(2π t); Alternatively, we could write d = 8 cos(2π t + π) or

d = 8 cos 2π( t + 1/2)