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egiven differential equation is a model of an undamped spring/mass sy

egiven differential equation is a model of an undamped spring/mass sy

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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d²x The given differential equation is a model of an undamped spring/mass system in which the restoring force F(x) in m + F(x) = 0 is nonlinear. dt² For the equation, use a numerical solver to plot the solution curves that satisfy the given initial conditions. X(t) x(t) 1.5 1.0 0.5 -0.5 -1.0 O-1.5 d²x dt² x(0) = 1, x'(0) = 1; x(0) = 2, x'(0) = -1 0.01x + xe 2 2 = 0, 6 period for x(0) = 2, x'(0) = -1 0.5 ANN 2 -0.5- t X(t) t 1.0 O-1.0 x(t) 1.5 1.0 0.5 -0.5 -1.0 O-1.5 If the solutions appear to be periodic, use the solution curve to estimate the period T of oscillations. (If the solution curve is not periodic, enter NOT.) period for x(0) = 1, x'(0) = 1
Transcribed Image Text:d²x The given differential equation is a model of an undamped spring/mass system in which the restoring force F(x) in m + F(x) = 0 is nonlinear. dt² For the equation, use a numerical solver to plot the solution curves that satisfy the given initial conditions. X(t) x(t) 1.5 1.0 0.5 -0.5 -1.0 O-1.5 d²x dt² x(0) = 1, x'(0) = 1; x(0) = 2, x'(0) = -1 0.01x + xe 2 2 = 0, 6 period for x(0) = 2, x'(0) = -1 0.5 ANN 2 -0.5- t X(t) t 1.0 O-1.0 x(t) 1.5 1.0 0.5 -0.5 -1.0 O-1.5 If the solutions appear to be periodic, use the solution curve to estimate the period T of oscillations. (If the solution curve is not periodic, enter NOT.) period for x(0) = 1, x'(0) = 1
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