Question

The distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds can be modeled by the graph below. Which equation is represented in the graph below?

On a coordinate plane, a curve crosses the y-axis at (0, negative 5). It increases to (1, 5) and then decreases to (2, negative 5). 5 cycles are shown.
d = negative 10 cosine (StartFraction pi Over 2 EndFraction t)
d = negative 10 cosine (pi t)
d = negative 5 cosine (StartFraction pi Over 2 EndFraction t)
d = negative 5 cosine (pi t)

Answer 1

d = negative 5 cosine (StartFraction pi Over 2 EndFraction t) [y=-5*cos(π/2)]

Explanation:

See the attached graph for the explanation. Desmos graphing software was used to plot the 4 equation options (using x in place of t and y in place of d).

The given points were added to see which of the graphed lines they best match. We can see that the third option, y=-5*cos(π/2), intersects all four points.

Two of the options (1st and 3rd) lie too close to y=0 to see their difference on the scale of the graph, so we can eliminate them. (Options 1 and 3)

Option 2 has an amplitude higher than the given points, so it can also be eliminated.

y=-5*cos(π/2) best represents the given points.