September 18th, 2006

freak

I had a screwed-up dream last night.

I was in a science classroom in my high school (I wanted to say my advisor's classroom, even though I never had her as a teacher, but for some reason it didn't look like her classroom. I just knew.) when I started to feel sort of funny. I went out the classroom, followed a hall (which was one of two halls to the classroom), and entered the nurse's office, which for some reason was connected to the science classroom.

Mum and Jeffrey were waiting for me there. The nurse entered for a few minutes and left. After the nurse left, Mum grabbed a syringe, held me down, and started to inject the stuff in my mouth. I fought back, but she pinned me down in the end and injected the stuff in my cheek. Jeffrey just stood back and watched. I pushed her away and ran back to the classroom to sit down. My stomach began to feel funny. I fell to the floor and felt no more.

Then I woke up with a funny feeling in my stomach.

Now, what? That's even more screwed up than the one with the airplanes.
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math: hypotamoose

I promised Ryan this earlier, so here you go. *hands it to him*

During the dead part of work today, I flipped through the calc book and found this problem in the DE chapter.

Juliet is in love with Romeo, who happens (in our version of the story) to be a fickle lover. The more Juliet loves him, the more he begins to dislike her. When she hates him, his feelings for her warm up. On the other hand, her love for him grows when he loves her and withers when he hates her. A model for this ill-fated romance is

dj/dt = Ar
dr/dt = -Bj,

where A and B are positive constants, r(t) represents Romeo's love for Juliet, and j(t) represents Juliet's love for Romeo at time t. (Negative love represents hate.)

a) The constant on the right hand side of Juliet's equation (dj/dt) has a positive sign, while the constant in Romeo's equation is negative. Explain why this follows from the story.

b) Derive a second-order differential equation for r(t) and solve it. (Your equation should involve r and its derivatives, but not j and its derivatives.)

c) Express r(t) and j(t) as functions of t, given r(0)=1 and j(0)=0. Your answer will contain A and B.

d) As you may have discovered, the outcome of the relationship is a never-ending cycle of love and hate. Find what fraction of the time they both love each other.


*snickers* Come to think of it, this describes at least one (out of not very many) of my past romantic relationships fairly accurately. Now to hope for a better model for any future relationships.
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