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

This is about graph of simple harmonic motion.

y(t) = a sin (ωt)

y(t) = A sin ωt

Where;

A is amplitude

ω is angular frequency

y(t) is the displacement at time(t)

ω can also be expressed as;

ω = 2π/T

Where T is period.

Thus;

y(t) = A sin (2π/T)t

Period; T = 2π/ω

Thus

y(t) = A sin (2π/(2π/ω))t

2π will cancel out to give;

y(t) = A sin (ωt)

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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)

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1/4 is the answer if i recall correctly.