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I have just started reading of "finite element model updating" which is a statistical means of updating the finite element model when there is source of uncertainty in the modelling parameters, modelling error, etc.

My question below is NOT related to finite element model updating but to a free vibration problem of linear spring with 100 degrees of freedom. I came across this problem whilst reading a text book on the subject of "Finite element model updating"

Let us consider a 100 degree of freedom system linear spring as shown in the figure below;

The figure below shows the free vibration of a mass M50 located in the middle.

**Note: Initial conditions - zero initial conditions except that the mass at the right end has an initial displacement of 0.01 m.**

The figures below zoom into the first and last 5 seconds of the response.

**First 5 seconds**

Last 5 seconds

Last 5 seconds

Following points may be observed from the above figures (as stated in the text I am reading)

1) Response of first 0.6 seconds was almost 0 since the wave has not yet arrived

My question: What is the wave that the author talks about here?

2) After the first wave arrived, the respond reached maximum and decayed rapidly

My question: Again what is this first wave? It is a free vibration problem. There is no damping in the model. Why does the response decay?

3) If the response of the last 5 seconds is taken, you get random response.

What is the reason of behaviour 1,2 and 3 ?

IS it a redundant problem with insufficient information?

Is it an incorrectly formulated problem?

Please can anyone help?

1) Response of first 0.6 seconds was almost 0 since the wave has not yet arrived

My question: What is the wave that the author talks about here?

2) After the first wave arrived, the respond reached maximum and decayed rapidly

My question: Again what is this first wave? It is a free vibration problem. There is no damping in the model. Why does the response decay?

3) If the response of the last 5 seconds is taken, you get random response.

What is the reason of behaviour 1,2 and 3 ?

IS it a redundant problem with insufficient information?

Is it an incorrectly formulated problem?

Please can anyone help?