- #1

Trying2Learn

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- TL;DR Summary
- Justify common frequency, yet different amplitudes

Hello!

Suppose you have two masses, that are connected by a spring.

Each mass is, in turn, connected by a spring to a wall

So there is a straight line: left wall to first mass, first mass to second mass, second mass to right wall

This problem can be analyzed as an eigenvalue problem.

We assume a solution for the displacement of each mass as:

x1(t) = X1 exp(i*omega*time)

x2(t) = X2 exp(i*omega*time)

Do you see that?

We

So my question is: can someone justify this assumption?

I know the process works and we must solve for an eigenvalue problem.

But could someone provide (in words), a justification for this

Suppose you have two masses, that are connected by a spring.

Each mass is, in turn, connected by a spring to a wall

So there is a straight line: left wall to first mass, first mass to second mass, second mass to right wall

This problem can be analyzed as an eigenvalue problem.

We assume a solution for the displacement of each mass as:

x1(t) = X1 exp(i*omega*time)

x2(t) = X2 exp(i*omega*time)

Do you see that?

We

**assume**a solution with:- an unspecified
frequency*common* - two
amplitudes*different*

So my question is: can someone justify this assumption?

I know the process works and we must solve for an eigenvalue problem.

But could someone provide (in words), a justification for this

**assumption**?