why it is particular solution + general solution?
why it is particular solution + general solution?
(OP)
Hi,
As to forced frequcncy analysis, theoretically it is to solve 2nd differential equation and the solutoin would be summation of general solution and particular solution, which I can understand exactly as this behavior is just the sum of transient and steady phonenomenon. However apart from vibration analysis and think about mathmatics only, is general solution plus particular solution always the solution for any 2nd differential equation? Only general solution can be the answer to some 2nd differential equation?
As to forced frequcncy analysis, theoretically it is to solve 2nd differential equation and the solutoin would be summation of general solution and particular solution, which I can understand exactly as this behavior is just the sum of transient and steady phonenomenon. However apart from vibration analysis and think about mathmatics only, is general solution plus particular solution always the solution for any 2nd differential equation? Only general solution can be the answer to some 2nd differential equation?





RE: why it is particular solution + general solution?
RE: why it is particular solution + general solution?
Homogenous solution applies to the unforced system.
Particular solution applies to the forced system.
The complete solution is the sum of the homogenous solution(s) and the particular solution. There are undetermined coefficients of the complete solution that will be evaluated based on the boundary conditions.
Homogenous solution is all you need if you wish to only study the unforced response of a system (starting at some non-zero initial condition).
But it won't tell you what happens when you apply a forcing funciton... that requires the particular solution.
Hope I said it right.... if not hope someone will correct me.
RE: why it is particular solution + general solution?
RE: why it is particular solution + general solution?