Question

When Eve released a spring, it completed one oscillation (cycle) per second and traveled up to 4 inches from equilibrium (its midline). She knows oscillation can be described by a cosine function with no horizontal or vertical displacement. Write an equation to describe this function.

A. y(t) = 4cos(2πt)
B. y(t) = 2cos(πt)
C. y(t) = 4cos(πt)
D. y(t) = 8cos(2πt)

Answer 1

The equation that describes the oscillation of the spring is y(t) = 4cos(2πt).

Step-by-step explanation:

The equation that describes the oscillation of the spring is y(t) = 4cos(2πt). This equation represents a cosine function because the description of the oscillation states that there is no horizontal or vertical displacement, which aligns with the cosine function. The amplitude of the motion is 4 inches, and the period is one second, which is why the equation includes 2π in the argument of the cosine function. Option A, y(t) = 4cos(2πt), is the correct equation to describe this function.