Sushi (sushimustwrite) wrote,
Sushi
sushimustwrite

  • Mood:
  • Music:

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.
Tags: math, mlc
Subscribe

  • The Accidental Mathematician

    You may know that I'm a writer who does math, but the interesting story is how this happened. I didn't suffer from a head injury that made me like…

  • (no subject)

    Work has been interesting. I've been getting used to waking up earlier to collect questionnaires and stuff from everyone. I've been around, though,…

  • I don't think the stars can tell me that.

    I have an Onion calendar from 2009. Since it's no longer 2009, I've been using the pages as a notepad when the need to scribble down directions or a…

  • Post a new comment

    Error

    Anonymous comments are disabled in this journal

    default userpic

    Your reply will be screened

    Your IP address will be recorded 

  • 0 comments