Question

The displacement from equilibrium of an object in harmonic motion on the end of a spring is given by y(t) = 1/3cos12t-1/4sin12t, where y is measured in feet and t is the time in seconds. determine the average velocity on the interval [pi/8, pi/3].

a. 0.216506
b. 0.288675
c. 0.433012
d. 0.866025

Answer 1

To find the average velocity of an object in simple harmonic motion on the interval [pi/8, pi/3], we use the displacement function y(t) to determine the displacements at the endpoints and then calculate the difference over the length of the interval.

Step-by-step explanation:

The student has asked to determine the average velocity of an object in simple harmonic motion over a given time interval. To find the average velocity, we must evaluate the displacement function at the endpoints of the interval and then divide the difference in displacements by the length of the interval. The displacement function given is y(t) = 1/3cos12t - 1/4sin12t, measured in feet with t as time in seconds.

To find the displacement at t = pi/8 and t = pi/3, we substitute these values into the displacement function to get y(pi/8) and y(pi/3). The average velocity v_avg over the interval [pi/8, pi/3] is then calculated using the formula:

v_avg = (y(pi/3) - y(pi/8)) / (pi/3 - pi/8).