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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 12CR

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