Good day everyone,
Until now I cannot move on with these two problems. I don't even know where to start . Anywhere, here goes:
1.) At time t, a pendulum makes an angle x(t) with the vertical axis. Assuming there is no friction, the equation of motion is
where m is the mass and l is the length of the string. Use the Runge-Kutta method to solve the differential equation over the interval [0, 2] using M = 40 steps and h = 0.05 if g = 32 ft/secē and
(a) ft and and
(a) ft and and
My concerns for this problem are that
(1) Am i supposed to integrate so that x'' becomes x' and then proceed with the iteration process?
(2) I am having a hard time trying to figure out the iteration for this problem since x(t) is not represented as an equation.
2.) Predator-Prey model. An example of a system of nonlinear differential equations is the predator-prey problem. Let x(t) and y(t) denote the population of rabbits and foxes, respectively at time t. The predator-prey model asserts that x(t) and y(t) satisfy
A typical computer simulation might use the coefficients
A = 2, B = 0.02, C = 0.0002, D = 0.8.
Use the Runge-Kutta method to solve the differential equation over the interval [0, 5] using M = 50 steps and h = 0.1 if
(a) rabbits and foxes
(b) rabbits and foxes
I basically have the same concern as the first problem. Both x(t) and y(t) are not represented as equations, but as functions alone.
I just need someone to help me start with the two problems .
From the RK4 equation, I'm supposed to solve for and to use the equation below:
I understand that is solved by getting and that . From here I don't know how to proceed since I don't know what values to fill in for . Just looking at the equations make me so confused.