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A certain physical system is governed by second-order initial value problem of the form a"(t) – 4.r'(t)+3r(t) =0 with r(0) = 1 and r'(0) = -2 %3D %3D (a) Write down the equivalent system of two first-order equations. (b) Use the fourth order Runge-Kutta method to solve the x(0.5) with step size h = 0.5

A certain physical system is governed by second-order initial value problem of the form a"(t) – 4.r'(t)+3r(t) =0 with r(0) = 1 and r'(0) = -2 %3D %3D (a) Write down the equivalent system of two first-order equations. (b) Use the fourth order Runge-Kutta method to solve the x(0.5) with step size h = 0.5

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A certain physical system is governed by second-order initial value problem of the form a"(t) – 4.x'(t) +3r(t) = 0 with (0) = 1 and (0)= -2 %3D %3D (a) Write down the equivalent system of two first-order equations. (b) Use the fourth order Runge-Kutta method to solve the x(0.5) with step size h = 0.5 %3D
Transcribed Image Text:A certain physical system is governed by second-order initial value problem of the form a"(t) – 4.x'(t) +3r(t) = 0 with (0) = 1 and (0)= -2 %3D %3D (a) Write down the equivalent system of two first-order equations. (b) Use the fourth order Runge-Kutta method to solve the x(0.5) with step size h = 0.5 %3D
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