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

Physics

Stella

3 February, 07:24

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.)

+4

Answers (1)

Know the Answer?

Russell Schwartz · 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