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CONCEPTUAL QUESTIONS:
-Does the Homogenous Solution represent the Transient Response?
Let me specify. For a N-DOF spring, mass, and damper mechanical system:
-Does the Homogenous Solution represent the Transient Response for given mechanical system?
MY ANSWER:
Yes.
ASSUMPTIONS:
-only stable systems are considered
WHERE I AM GETTING CONFUSED:
According to Swarthmore University [Link listed]: http://lpsa.swarthmore.edu/Transient/TransZIZStime.html
QUOTE:
Finding the homogeneous and particular solutions is a general technique for solving differential equations of the sort that we will encounter (different inputs require different forms of the particular response, but we will only consider step inputs (i.e., the input is constant for t>0) for now. However, contemplation of the technique begs the question: What, physically, do the homogeneous and particular response represent. The particular response represents the response of the system after any initial transients have died out, but the the homogeneous response doesn't really represent anything physical. The reason we use it is that it is mathematically correct and yields the right answer.
END QUOTE. (You can search that and Cltrl F (Command F) and paste that quote to find where this is listed)
Please note:
If their statement is only applicable to electrical systems. Then can you tell me how?
-Does the Homogenous Solution represent the Transient Response?
Let me specify. For a N-DOF spring, mass, and damper mechanical system:
-Does the Homogenous Solution represent the Transient Response for given mechanical system?
MY ANSWER:
Yes.
ASSUMPTIONS:
-only stable systems are considered
WHERE I AM GETTING CONFUSED:
According to Swarthmore University [Link listed]: http://lpsa.swarthmore.edu/Transient/TransZIZStime.html
QUOTE:
Finding the homogeneous and particular solutions is a general technique for solving differential equations of the sort that we will encounter (different inputs require different forms of the particular response, but we will only consider step inputs (i.e., the input is constant for t>0) for now. However, contemplation of the technique begs the question: What, physically, do the homogeneous and particular response represent. The particular response represents the response of the system after any initial transients have died out, but the the homogeneous response doesn't really represent anything physical. The reason we use it is that it is mathematically correct and yields the right answer.
END QUOTE. (You can search that and Cltrl F (Command F) and paste that quote to find where this is listed)
Please note:
If their statement is only applicable to electrical systems. Then can you tell me how?