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For given system the equation of motion is: x+x-2x=0 With initial conditions: x(0) = 3 mm; x(0) = 0mm/sec #1 By guessing solution in a form x(t) = e₁t solve this equation following these steps Write characteristic equation, define eigenvalues, write general solution, calculate coefficients and finally present particular solution. Represent this second order differential equation as a system of first order differential equations. Explain your steps. #2 Represent this second order differential equation as a system of first order differential equations. Explain your steps. #3 Can you predict what happen with your system when time approaches to infinity? Can you say that system is stable? Explain your considerations

For given system the equation of motion is: x+x-2x=0 With initial conditions: x(0) = 3 mm; x(0) = 0mm/sec #1 By guessing solution in a form x(t) = e₁t solve this equation following these steps Write characteristic equation, define eigenvalues, write general solution, calculate coefficients and finally present particular solution. Represent this second order differential equation as a system of first order differential equations. Explain your steps. #2 Represent this second order differential equation as a system of first order differential equations. Explain your steps. #3 Can you predict what happen with your system when time approaches to infinity? Can you say that system is stable? Explain your considerations

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter2: Vectors
Section: Chapter Questions
Problem 37P: Assuming the +x -axis is horizontal and points to the tight, resolve the vectors given In the...
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For given system the equation of motion is: x+x-2x=0 With initial conditions: x(0) = 3 mm; x(0) = 0mm/sec #1 By guessing solution in a form x(t) = e₁t solve this equation following these steps Write characteristic equation, define eigenvalues, write general solution, calculate coefficients and finally present particular solution. Represent this second order differential equation as a system of first order differential equations. Explain your steps. #2 Represent this second order differential equation as a system of first order differential equations. Explain your steps. #3 Can you predict what happen with your system when time approaches to infinity? Can you say that system is stable? Explain your considerations
Transcribed Image Text:For given system the equation of motion is: x+x-2x=0 With initial conditions: x(0) = 3 mm; x(0) = 0mm/sec #1 By guessing solution in a form x(t) = e₁t solve this equation following these steps Write characteristic equation, define eigenvalues, write general solution, calculate coefficients and finally present particular solution. Represent this second order differential equation as a system of first order differential equations. Explain your steps. #2 Represent this second order differential equation as a system of first order differential equations. Explain your steps. #3 Can you predict what happen with your system when time approaches to infinity? Can you say that system is stable? Explain your considerations
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