For seconds, the height (in meters) of a mass oscillating on a vertical spring is…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

For

0 \le t \le \pi

seconds, the height (in meters) of a mass oscillating on a vertical spring is modeled by

s(t)=3\sin(2t)+5.

Use this model to explore the motion of the mass. (a) Find the velocity function

v(t)

for

0 \le t \le \pi

and state its units. (b) Evaluate

v\!(\frac{\pi}{6})

and interpret the meaning of this value in the context of the oscillation. (c) Determine all times in the interval

0 \le t \le \pi

at which the mass is momentarily at rest. (d) Identify each sub-interval on

[0,\pi]

during which the mass is moving upward and each during which it is moving downward. Support your answer with appropriate reasoning.