Help: Differential equation Romeo & Juliet

In summary, the differential equation concept that best captures the idea of Romeo's and Juliet's fancies turning to thoughts of love in the spring is an unstable equilibrium.
  • #1
helpmath
3
0
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(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 the answer is A, but I’m not completely sure why.
 
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  • #2
Hello, and welcome to MHB! (Wave)

You may wish to read the following two threads first:

https://mathhelpboards.com/calculus-10/differential-equations-romeo-juliet-24978.html

https://mathhelpboards.com/calculus-10/romeo-juliet-initial-conditions-24991.html
 
  • #3
MarkFL said:
Hello, and welcome to MHB! (Wave)

You may wish to read the following two threads first:

https://mathhelpboards.com/calculus-10/differential-equations-romeo-juliet-24978.html

https://mathhelpboards.com/calculus-10/romeo-juliet-initial-conditions-24991.html

Hi, thank you for the links!
Sorry, I believe I should have made the title of my question more clear.
I have some trouble with the last part of the assignment, as I don't completely understand what forcing a term is and how it relates to the quote.

Would you be able to help me? (If you don't mind)

Thanks!
 
  • #4
helpmath said:
Hi, thank you for the links!
Sorry, I believe I should have made the title of my question more clear.
I have some trouble with the last part of the assignment, as I don't completely understand what forcing a term is and how it relates to the quote.

Would you be able to help me? (If you don't mind)

Thanks!

A forcing term, or forcing function, is broadly a function that appears in the equations and is only a function of time, and not of any of the other variables. A forcing term in this problem, appears to be the result of Romeo's love being influenced seasonally, that is, during the spring. Since the term "seasonally" refers only to time, and not to any of the other variables in the system, this seasonal influence would be mathematically modeled by a forcing function. I think that's what you're being asked to observe here.
 
  • #5
MarkFL said:
A forcing term, or forcing function, is broadly a function that appears in the equations and is only a function of time, and not of any of the other variables. A forcing term in this problem, appears to be the result of Romeo's love being influenced seasonally, that is, during the spring. Since the term "seasonally" refers only to time, and not to any of the other variables in the system, this seasonal influence would be mathematically modeled by a forcing function. I think that's what you're being asked to observe here.

Thank you so much!
 

Related to Help: Differential equation Romeo & Juliet

1. What is a differential equation?

A differential equation is a mathematical equation that involves one or more derivatives of an unknown function. It is used to describe relationships between quantities that are continuously changing.

2. How are differential equations used in Romeo & Juliet?

In Romeo & Juliet, differential equations can be used to model the relationship between the characters' emotions and actions. For example, the famous balcony scene can be described using a differential equation to show how Romeo's feelings for Juliet change over time.

3. What is the significance of using differential equations in literature?

Differential equations can be used to analyze and understand complex relationships and behaviors in literature. By using mathematical models, we can gain new insights into the characters' motivations and actions.

4. Can differential equations be solved for real-life situations?

Yes, differential equations are widely used in various fields such as physics, engineering, and economics to solve real-life problems. In literature, they can be used to explore human behavior and relationships in a more quantitative manner.

5. Are there any limitations to using differential equations in literature?

While differential equations can provide valuable insights, they are not a perfect tool for analyzing literature. They can oversimplify complex human emotions and interactions, and may not fully capture the nuances of a literary work. Therefore, they should be used in conjunction with other methods of literary analysis.

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