- #1

martha1

- 4

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*Consider the system dr/dt = -j, dj/dt = r , where r (t) represents Romeo’s love (positive values) or hate (negative*

values) for Juliet at time t, and j(t) similarly represents Juliet’s feelings toward Romeo

values) for Juliet at time t, and j(t) similarly represents Juliet’s feelings toward Romeo

The first question I was able to answer:

*(a)*

**Juliet**“loves to be loved,” while**Romeo**is intrigued by rejection.However, at the second question I am kinda lost:

*(b) Romeo’s and Juliet’s families are enemies. This can be expressed in the initial condition (r, j) = (.,.) at time t = 0.*

Because it is also an online exercise we need to do, I know both values need to be either -1,0 or 1. I also assume this has to do with the the solution having the form of a sinus wave, but I am not sure what the reasoning behind this. Also, I assume that one of the values is -1, as they are enemies and -1 represents hate, but I am not sure if this is the case for Juliet or Romeo and what then the other value should be.

Then, they continue with this question:

*(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 but

never at the same time.

- They end up being in love.

- They end up not being in love.

- None of the above.

- 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 but

never at the same time.

- They end up being in love.

- They end up not being in love.

- None of the above.

Which can probably also be explained with a visual representation (in sinus form) of the solution, but again, I don't understand what the reasoning behind it being a sinus wave is and also how exactly the solution would look when graphed. As I need to explain this problem in class, it would be really great if someone could explain it to me.

Any help is welcome, thanks!