- #1

Trying2Learn

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- TL;DR Summary
- Why assume exponential

Consider a free vibration problem of a mass in 1D: inertia, damping, spring, and no forcing function.

We begin by assuming an exponential response.

And then run through all the cases of under, over, critical damping, etc.

I am fully aware of Euler's formula that relates sine/cosine to complex exponential, etc.

But when an analyst first attemps a solution of such a system, there is no

of what it leads to.

Can someone justify why we assume a trial exponential response to a free vibration problem?

The only answer I seem able to give is that: it works because Euler, complex, trig, etc.

(Forgive me for marking this "Advanced" I seek a more conceptual understandingFor example, could one say that the derivatives of the exponential are exponential and this serves as a basis for all possible functions?

We begin by assuming an exponential response.

And then run through all the cases of under, over, critical damping, etc.

I am fully aware of Euler's formula that relates sine/cosine to complex exponential, etc.

But when an analyst first attemps a solution of such a system, there is no

*a priori*knowedge about such issues -- just*a posteriori*knowledgeof what it leads to.

Can someone justify why we assume a trial exponential response to a free vibration problem?

The only answer I seem able to give is that: it works because Euler, complex, trig, etc.

(Forgive me for marking this "Advanced" I seek a more conceptual understandingFor example, could one say that the derivatives of the exponential are exponential and this serves as a basis for all possible functions?