I have a problem stating a frictionless rod has the equation of motion. d^2r/dt^2-4r=-9.81sin(2t).  I know that To=0, R0=0 and R'(0)= 2.4 How do i set up the formulas to calculate using Improved Euler method?

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
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I have a problem stating a frictionless rod has the equation of motion.

d^2r/dt^2-4r=-9.81sin(2t).  I know that To=0, R0=0 and R'(0)= 2.4

How do i set up the formulas to calculate using Improved Euler method? 

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This is very helpful and I'm close.  I am still having trouble seeing how to plug s into f(r,s) when s=r' and there is no r' in the original equation. 

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