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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.
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.