uation of motion in the form x(t) = Ae™it sin( V2 – 2?t + w), which ft

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A force of 13 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.6 times the instantaneous
velocity.
(a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position.
x(t) =
ft
(b) Express the equation of motion in the form x(t)
= Ae-it sin v@² – 2²t + @ ), which is given in (23) of Section 3.8. (Round o to two decimal places.)
x(t)
ft
(c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)
Transcribed Image Text:A force of 13 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.6 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Ae-it sin v@² – 2²t + @ ), which is given in (23) of Section 3.8. (Round o to two decimal places.) x(t) ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)
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