How Do You Solve the Coefficients for a Forced Oscillation Equation?

[MahaX]

Determine the forced oscillation of a system under a force F(t) = at, if at time t = 0, the system is at rest in equilibrium (x = x' = 0)



2. Equation of motion: x" + ω²x = at



3. I've found the particular solution, but i just can't find the coeficients of the homogeneous solution ( x = a cos (wt+θ) or x = Acos(wt) + Bsin(wt) )...

 

[ehild]

You get the coefficients of the homogeneous solution by using the initial conditions: Both X=Acos(wt)+Bsin(wt)+Xp and X' are equal to 0 at t = 0.

ehild