So, I need to give a presentation on this problem, but I'm quite stuck. It would be great if someone can help me out. This is what the assignment says:
Consider the system dr/dt = -j, dj/dt = r , where r (t)represents Romeo’s love (positive values) or hate (negativevalues) for Juliet at time t, and j(t) similarly representsJuliet’s feelings toward Romeo.
(a) Juliet “loves to be loved,” while Romeo is intrigued by rejection.
-- This question I understand and I was able to fill in, however the next one I don't.
(b) Romeo’s and Juliet’s families are enemies. This can be expressed in the initial condition (r, j) =(.,.) at time t = 0.
-- The values that I can give for both r and j are either -1,0 or 1, but I don't understand why and what the correct answer is here. I'm guessing at least one of them needs to be -1 (because of the fact of them being enemies at first), but that is as far as I get. The follow-up question is:
(c) What happens in the long run?
- They are mutually in love a quarter of the time.
- They are mutually in love half the time.
- They are sometimes in love with the other butnever at the same time.
- They end up being in love.
- They end up not being in love.
- None of the above.
- I know if you graph it you are supposed to get two sinus waves with a different phase (I read this somewhere on the internet), which probably explains this question as well as b), but I don't understand why this is the case.
Thanks for your help!
Consider the system dr/dt = -j, dj/dt = r , where r (t)represents Romeo’s love (positive values) or hate (negativevalues) for Juliet at time t, and j(t) similarly representsJuliet’s feelings toward Romeo.
(a) Juliet “loves to be loved,” while Romeo is intrigued by rejection.
-- This question I understand and I was able to fill in, however the next one I don't.
(b) Romeo’s and Juliet’s families are enemies. This can be expressed in the initial condition (r, j) =(.,.) at time t = 0.
-- The values that I can give for both r and j are either -1,0 or 1, but I don't understand why and what the correct answer is here. I'm guessing at least one of them needs to be -1 (because of the fact of them being enemies at first), but that is as far as I get. The follow-up question is:
(c) What happens in the long run?
- They are mutually in love a quarter of the time.
- They are mutually in love half the time.
- They are sometimes in love with the other butnever at the same time.
- They end up being in love.
- They end up not being in love.
- None of the above.
- I know if you graph it you are supposed to get two sinus waves with a different phase (I read this somewhere on the internet), which probably explains this question as well as b), but I don't understand why this is the case.
Thanks for your help!