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Given: The equation of motion is: x + 3x + 2x = 0 With initial conditions: x(0) = 2 mm; x(0)=-3 mm/sec a) By guessing solution in a form x(t) = et solve this equation following these steps Write characteristic equation, define eigenvalues, write general solution, calculate coefficients and finally present particular solution. b) Represent this second order differential equation as a system of first order differential equations. Explain your steps. c) Write a MATLAB script to solve this equation numerically and plot x(t) for timespan from 0 to 10 sec

Given: The equation of motion is: x + 3x + 2x = 0 With initial conditions: x(0) = 2 mm; x(0)=-3 mm/sec a) By guessing solution in a form x(t) = et solve this equation following these steps Write characteristic equation, define eigenvalues, write general solution, calculate coefficients and finally present particular solution. b) Represent this second order differential equation as a system of first order differential equations. Explain your steps. c) Write a MATLAB script to solve this equation numerically and plot x(t) for timespan from 0 to 10 sec

Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter1: Matrices, Vectors, And Vector Calculus
Section: Chapter Questions
Problem 1.24P
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Given: The equation of motion is: x + 3x + 2x = 0 With initial conditions: x(0) = 2 mm; x(0)=-3 mm/sec a) By guessing solution in a form x(t) = et solve this equation following these steps Write characteristic equation, define eigenvalues, write general solution, calculate coefficients and finally present particular solution. b) Represent this second order differential equation as a system of first order differential equations. Explain your steps. c) Write a MATLAB script to solve this equation numerically and plot x(t) for timespan from 0 to 10 sec
Transcribed Image Text:Given: The equation of motion is: x + 3x + 2x = 0 With initial conditions: x(0) = 2 mm; x(0)=-3 mm/sec a) By guessing solution in a form x(t) = et solve this equation following these steps Write characteristic equation, define eigenvalues, write general solution, calculate coefficients and finally present particular solution. b) Represent this second order differential equation as a system of first order differential equations. Explain your steps. c) Write a MATLAB script to solve this equation numerically and plot x(t) for timespan from 0 to 10 sec
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