8. A weight of mass 8 kg is suspended by a spring with k = 10 N/ m and c = 1.6 N s/m. The initial displacement is 0 m and the initial velocity is 0) m/s. An external force F = t e' is applied to the mass. As this non linear differential equation can't be solved exactly with the tools demonstrated in Chapter 2, you must instead convert the second order differential equation into two first order differential equations and apply the RK4 numerical recursion formula with h = 0. 5. Do only one recursion where you generate the individual values of the k's and l's which you will use to approximate the displacement at t = 0. 5. Use four decimal point accuracy in all calculations. %3D

8. A weight of mass 8 kg is suspended by a spring with k = 10 N/ m and c = 1.6 N s/m. The initial displacement is 0 m and the initial velocity is 0) m/s. An external force F = t e' is applied to the mass. As this non linear differential equation can't be solved exactly with the tools demonstrated in Chapter 2, you must instead convert the second order differential equation into two first order differential equations and apply the RK4 numerical recursion formula with h = 0. 5. Do only one recursion where you generate the individual values of the k's and l's which you will use to approximate the displacement at t = 0. 5. Use four decimal point accuracy in all calculations. %3D

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

8. A weight of mass 8 kg is suspended by a spring with k = 10 N/ m and c = 1.6 N s/m. The initial
displacement is 0 m and the initial velocity is () m/s. An external force F = t e¯' is applied to the
%3D
mass. As this non linear differential equation can't be solved exactly with the tools demonstrated in
Chapter 2, you must instead convert the second order differential equation into two first order
differential equations and apply the RK4 numerical recursion formula with h = 0.5. Do only one
recursion where you generate the individual values of the k's and l's which you will use to
approximate the displacement at t = 0. 5.Use four decimal point accuracy in all calculations.

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