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Consider the dynamics of a mass on a spring, given by d²x(t) +kx = 0. dt² By setting y = x, reduce the second order ODE into a system of first order ODES. Then, find co-ordinates in which the 1st order system is diagonal and thus solve the system of equations. Plot the solution starting from non-zero initial conditions in the (x(t),y(t)) plane and interpret this solution in terms of the original mass on the spring.

Consider the dynamics of a mass on a spring, given by d²x(t) +kx = 0. dt² By setting y = x, reduce the second order ODE into a system of first order ODES. Then, find co-ordinates in which the 1st order system is diagonal and thus solve the system of equations. Plot the solution starting from non-zero initial conditions in the (x(t),y(t)) plane and interpret this solution in terms of the original mass on the spring.

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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Consider the dynamics of a mass on a spring, given by d²x(t) +kx = 0. dt2 By setting y=x, reduce the second order ODE into a system of first order ODES. Then, find co-ordinates in which the 1st order system is diagonal and thus solve the system of equations. Plot the solution starting from non-zero initial conditions in the (x(t),y(t)) plane and interpret this solution in terms of the original mass on the spring.
Transcribed Image Text:Consider the dynamics of a mass on a spring, given by d²x(t) +kx = 0. dt2 By setting y=x, reduce the second order ODE into a system of first order ODES. Then, find co-ordinates in which the 1st order system is diagonal and thus solve the system of equations. Plot the solution starting from non-zero initial conditions in the (x(t),y(t)) plane and interpret this solution in terms of the original mass on the spring.
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