# Large Amplitude Solutions in a forced massed spring system

1. May 12, 2013

### Kevin2341

"Large Amplitude Solutions in a forced massed spring system"

1. The problem statement, all variables and given/known data

Using the formula, y"+by'+k1*y+k2*h(y) = -10 +0.1sin(ωt)

In the previous part of the of this "lab", I had to use some conditions for b, k1, k2, and ω, and analytically solve the problem and compare the graphs of the solutions between my answer, and a computer generated solution of the given 2nd order DE. Now in this part, they want me to find "large amplitude solutions", to "help" me, they give me a picture of some form of what I would consider a topographical graph of the DE with specific values, b = 0.01, k1 = 13, k2 = 4, and ω = 4. In this "topographical map" of that specific set of values, there were these blue regions, and then these smaller and less frequent black regions. Within the black region large amplitude solutions were generated (the different parts of this map represented different initial conditions).

Here is a picture of what I'm talking about...

2. Relevant equations

3. The attempt at a solution

I'm at a loss here, the instructions in the book feel like the author was going on a rant about something and nobody knows what he was originally talking about. He then sends me on my way, and tells me it is "delicate work".

Has anyone seen anything like this before, or have any idea how to do this? This is is the last part of this lab which has been pretty straight forward, and then I hit this, and all of a sudden I am supposed to sit around and "guess" where my solutions might be? I don't like that, that's not math to me, that's bullgarbageting around until you think you find something that might work.