A mass ball m is abandoned from the home in a tube containing a high viscosity fluid. The fluıdo offers a resistance, R, to the movement proportional to its instantaneous velocity, that is, R = bv, where b is a constant.   a) Build an ODE based on Newton's second law, with respect to the velocity of the sphere in this fluid   b)What is the initial condition for this model?

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 mass ball m is abandoned from the home in a tube containing a high viscosity fluid. The fluıdo offers a resistance, R, to the movement proportional to its instantaneous velocity, that is, R = bv, where b is a constant.

 

a) Build an ODE based on Newton's second law, with respect to the velocity of the sphere in this fluid

 

b)What is the initial condition for this model?

 

c)Resolve the initial value problem formed by (a) and (b) using the Laplace transform and obtain an expression for ball speed as a function of time.

 

d) According to (c) what will be the maximum speed reached by this sphere?

 

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