Different type of differential question most ppl used to

[squirby]

hey guys. just wondering if anyone can help me out, this is a different type of question most ppl are used to.

"For a system, it is given that the complementary solution is 8exp(-3t)u(t).
The particular solution for the system is cos(4t)u(t). determine, in its simplest form, the forcing function, f(t), applied to the system"

basically, they are asking for you to determine the right hand side of a differential equation, and they haven't given us the left hand side. we can ignore u(t),it's the unit step function and since we are only solving for t greater than zero this can be ignored.

just wondering, can anyone give me steps to solving this? I'm desperate... can't find a similar type of question anywhere. thanks heaps for any input guys!

 

[LCKurtz]

Well, if exp(-3t) is a solution of the homogeneous equation then its characteristic equation would be r + 3 = 0 so the homogeneous equation would be:

y' + 3y = 0

Now put y = cos(4t) in that equation to see what the right side needs to be.