An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is

s = 8 cos t + 9 sin t, t ≥ 0,

where s is measured in centimeters and t in seconds. (Take the positive direction to be downward.)

1) How far from its equilibrium position does the mass travel? (Round your answer to two decimal places.)

Question

Lucille Avery

Physics

19 August, 23:33

An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is

s = 8 cos t + 9 sin t, t ≥ 0,

where s is measured in centimeters and t in seconds. (Take the positive direction to be downward.)

1) How far from its equilibrium position does the mass travel? (Round your answer to two decimal places.)

+3

Answers (1)

Know the Answer?

Georgia · Answer 1

To get that, find the time when slope equals to 0, use the derivate theory from calculus.

s = 8 cos t + 9 sin t, t ≥ 0

s' = - 8 sin t + 9 cos t (this is slope)

0 = - 8 sin t + 9 cos t

8 sin t = 9 cos t

tan t = 9/8

t = 48.37 seconds