- #1
arizonian
- 18
- 2
I feel so embarrased asking this question, but this is the place to get answers.
I have a 2nd order ODE with a forcing function that needs to be manipulated and put into a matrix for a numerical method solution, ie Matlab. My question is: Is the matrix composed of a particular solution in the top row and a homogenous solution in the bottom row? Does this satisfy the requirement for two equations? Maybe I should say equation, not solution.
My work:
m d^2x/dt^2 + c dx/dt + kx = 0
d^2x/dt^2 = dx/dt
Substituting y2 for d^2t/dx^2 and y1 for dx/dt, and realizing that y2 is the derivative of y1, I end up with, in matrix form:
(I am using periods to hold the spacing)
[-1/k...-c/mk]..[y2]...=[x2]
[1...-1]..[y1]...=[x1]
Thank you
Bill
On edit, I realized I forgot the signs in the first equation.
On second edit, I changed the lower equation to simplify what I was after.
I have a 2nd order ODE with a forcing function that needs to be manipulated and put into a matrix for a numerical method solution, ie Matlab. My question is: Is the matrix composed of a particular solution in the top row and a homogenous solution in the bottom row? Does this satisfy the requirement for two equations? Maybe I should say equation, not solution.
My work:
m d^2x/dt^2 + c dx/dt + kx = 0
d^2x/dt^2 = dx/dt
Substituting y2 for d^2t/dx^2 and y1 for dx/dt, and realizing that y2 is the derivative of y1, I end up with, in matrix form:
(I am using periods to hold the spacing)
[-1/k...-c/mk]..[y2]...=[x2]
[1...-1]..[y1]...=[x1]
Thank you
Bill
On edit, I realized I forgot the signs in the first equation.
On second edit, I changed the lower equation to simplify what I was after.
Last edited: