Question

The displacement from equilibrium of a weight oscillating on the end of a spring is given by y = 1.93 - 0.220 cos(4.90), where y is the displacement (in feet) and is the time (in seconds). Use a graphing utility to graph the displacement function for Osts 10. Find the time beyond which the distance between the weight and equilibrium does not exceed 0.9 ft. (Round your answer to 2 decimal places.)

A) Graph the displacement function
B) Find the time beyond which the distance doesn't exceed 0.9 ft
C) The distance never exceeds 0.9 ft
D) There is insufficient information to determine the time

Answer 1

To graph the displacement function and find the time when the distance does not exceed 0.9 ft from equilibrium, we must plot the provided oscillatory function and solve the inequality involving the amplitude and given constraints.

Step-by-step explanation:

The question describes the oscillatory motion of a mass on a spring where the displacement from equilibrium is given by y = 1.93 - 0.220 cos(4.90t), with y in feet and t in seconds. For the task at hand, we would graph this displacement function over a time period of 0 to 10 seconds using a graphing utility.

To determine the time beyond which the distance between the weight and equilibrium does not exceed 0.9 feet, we must solve the inequality |1.93 - 0.220 cos(4.90t)| ≤ 0.9. We would use algebraic methods and a graphing calculator to find the times t that satisfy this condition. If the amplitude is continuously greater than 0.9, the distance will never be within 0.9 ft of equilibrium, which will lead us to determine if the statement 'C) The distance never exceeds 0.9 ft' is true.