An object is in simple harmonic motion with amplitude a and period 2π/ω. Find an equation that models the displacement y at time t under the given condition. y = 0 at time t = 0

y (t) = a sin (ωt).

Step-by-step explanation:

The graph of the motion starts at y-0 t = 0 so we use sine in the equation

y (t) = A sin (2π t / T) where A = the amplitude and T = the period so here we can write:

Displacement at t = y (t) = a sin (2π / 2π/ω) t

y (t) = a sin (ωt)