Answered: x>0 Equilibrium -- position -x = 0 x<0…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 15RE

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Question

Spring oscillations A spring hangs from the ceiling at equilibrium
with a mass attached to its end. Suppose you pull downward on
the mass and release it 10 inches below its equilibrium position
with an upward push. The distance x (in inches) of the mass from
its equilibrium position after t seconds is given by the function
x(t) = 10 sin t - 10 cos t, where x is positive when the mass is
above the equilibrium position

a. Graph and interpret this function.
b. Find dx/dt and interpret the meaning of this derivative.
c. At what times is the velocity of the mass zero?
d. The function given here is a model for the motion of an object
on a spring. In what ways is this model unrealistic?

x>0
Equilibrium --
position
-x = 0
x<0
M

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