# Help: Differential equation Romeo & Juliet

• MHB
helpmath
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.

Gold Member
MHB
Hello, and welcome to MHB! (Wave)

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

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

helpmath
Hello, and welcome to MHB! (Wave)

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!

Gold Member
MHB
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.

helpmath
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!