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

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.)

anonymous · Answer

Is the q asking to find the farthest point the mass traveled?
If so, it would help to think of it as a graph. The furthest it would be from eq will be either the maximum or minimum point, depending on which one is further

To get that, find the time when slope equals to 0

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

continue from there :)