Romeo and Juliet equations: dr/dt = -j, dj/dt = r

martha

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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!
 
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!
Are you being taught "Ordinary Differential Equation"?
 
Are you being taught "Ordinary Differential Equation"?

I do still have a question if you don't mind helping! I managed to solve it by using the initial condition (-1,-1) as someone told me to do, however I don't understand exactly the reason behind this.
I get that the values should be negative because the families are enemies, but why -1 and not for example -1.4?
I've plotted my solutions :
r(t)= sin(t)-cos(t)
j(t)=-cos(t)-sin(t)

And the minimum is below -1, so how could I have known that the initial condition is (-1,-1)?

Many thanks!
 
Help: Differential equation Romeo & Juliet

Hi, I have to make an assignment on differential equations and Romeo and Juliet.
r(t) is romeo's love for Juliet at time t, j(t) is Juliet's love for Romeo at time t
So far, it is given: dr/dt=-j and dj/dt=r.
It is also given that Romeo & Juliet's families are enemies, thus the initial condition at time t=0 is (r,j)=(-1,-1)


If we would take the second derivative of r we get: r’’=-j’. We know that j’=r, which means r’’ =-r. can be recognized as the equation of an harmonic oscillator. Our solution will therefore have this shape: r=A sin(t)+B cos(t).
To get the solution to j, we know j=-r’, which gives us:
j= -(Acos(t)-Bsin(t))= -Acos(t)+Bsin(t)
With the initial conditions r(0)=-1 and j(0)=-1:
r(t)= sin(t)-cos(t)
j(t)=-cos(t)-sin(t)


Now, the last part of the assignment is:
“In the Spring a young man’s fancy lightly turns to thoughts of love,” says Tennyson.
What differential equation concept is best invoked to capture this
idea?
A. a forcing term
B. an unstable equilibrium
C. a nonlinear function for t
D. none of the above


Could someone help me with this part? I know it's A, but I don't know why
 
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