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.)

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