Answered: x(1) Consider a mass-spring-dashpot…

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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Consider a mass–spring–dashpot system which is modelled by
mx
00
+ cx
0
+ kx = f(t) with the initial conditions x (0) = 0, x
0
(0) = 1 where the imposed external force
is f(t) = 2sin(2t), the mass is m = 1, the spring constant is k = 8, and the dashpot impedance is c = 6.
To find the position function x(t), please solve the following equation:
By LAPLACE TRANSFORM METHOD, solve step by step the IVP
x
00 + 6x
0
+ 8x = 2sin (2t), x (0) = 0, x
0
(0) = 1.

f(t)
x(1)
Consider a mass-spring-dashpot system which is modelled by
ma" + ca' + ka = f(t) with the initial conditions r (0) = 0, x' (0) = 1 where the imposed external force
is f(t) = 2sin(2t), the mass is m = 1, the spring constant is k = 8, and the dashpot impedance is c= 6.
To find the position function r(t), please solve the following equation:
%3|
By LAPLACE TRANSFORM METHOD, solve step by step the IVP
x" + 6x' + 8x = 2sin (2t), x (0) = 0, x' (0) = 1.
(The answers including other methods will be worth "zero" points)

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