Question

A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the frequency of the system is 6/π cycles per second, determine a trigonometric model that gives the position of the weight at time t seconds.

A. y = –5 cos 12t
B. y = 5 cos 12t
C. y = –5 cos 6t
D. y = 5π cos 6t

Answer 1

The correct trigonometric model for a weight attached to a spring and oscillating with a frequency of 6/π cycles per second is represented by y = –5 cos(12t), as it accounts for the amplitude, angular frequency, and initial displacement.

Step-by-step explanation:

The student is dealing with a physics problem involving simple harmonic motion (SHM). Since the system is oscillating with a specific frequency, we can model the position of the mass as a function of time using a trigonometric function. The frequency given is 6/π cycles per second, which means the angular frequency ω is 2π * frequency, resulting in an angular frequency of 12 radians per second. The weight is pulled down 5 inches, indicating that the amplitude (A) of oscillation is 5 inches. The negative sign in a cosine function represents a phase shift of π, which is necessary because the weight starts 5 inches below the equilibrium position. Therefore, the correct trigonometric model for this system is y = –5 cos(12t), making Option A the correct choice.