Starting a New research Lab. Need help with this

[Shandra2]

Homework Statement

X" + X = 2Asin (t - 8)

Homework Equations

The Attempt at a Solution

I don't really even know where to begin. I got this lab as just an assistant and it's just something they were talking about and I'm not really sure how to start.

 

[hunt_mat]

You have you particular solution and your general solution. The general solution is trhe solution of $$\ddot{x}+x=0$$ and I would look for a particular solution of the form:

$$x_{p}=\alpha\cos (t-8)+\beta\sin (t-8)$$

The solution will be the sum of your particular and general solutions.

 

[LCKurtz]

Homework Statement

X" + X = 2Asin (t - 8)

Homework Equations

The Attempt at a Solution

I don't really even know where to begin. I got this lab as just an assistant and it's just something they were talking about and I'm not really sure how to start.

You have you particular solution and your general solution. The general solution is trhe solution of $$\ddot{x}+x=0$$ and I would look for a particular solution of the form:

$$x_{p}=\alpha\cos (t-8)+\beta\sin (t-8)$$

The solution will be the sum of your particular and general solutions.

But that won't work. Those two functions are solutions of the homogeneous equation just like the {sin(t), cos(t)} pair. Better to try

$$x_{p}=\alpha t\cos (t-8)+\beta t\sin (t-8)$$

 

[hunt_mat]

Yep, you're absolutly correct. What was I thinking? Brain on automatic I suppose.

 

[Shandra2]

Can you explain to me how you get there? I appreciate you taking the time on something which isn't really that serious. I just want to understand this more.

 

[LCKurtz]

Can you explain to me how you get there? I appreciate you taking the time on something which isn't really that serious. I just want to understand this more.

You can google for undetermined coefficients. Or a more detailed explanation describing the method of annihilators is at

http://faculty.swosu.edu/michael.dougherty/DiffEqI/lecture10.pdf

Hopefully you have studied constant coefficient differential equations in the past so the reading won't be too intimidating.