Calculating damping ratio using the log-decrement method

I received the following question:

"To calculate the damping coefficient is it sufficient to use, damping ratio = delta / sqrt(4*pi^2 + delta^2), where delta = 1 / n * ln(B1 / Bn+1), and B1 is a peak of the wave followed by Bn+1 being a peak of the wave "n" cycles way, is this an acceptable method to use?"

This is the log-decrement method mentioned in the Lab 2 lecture slides, and is definitely one method to calculate damping ratio. In general, the lectures given on Monday (and to some extent on Friday) are always going to pertain to methods and theory you will need to complete your lab reports. Obviously, the Friday lectures are more geared towards the TechCom side of the report.

Actually, this brings up an overarching issue for a new sticky I will post in the Lab 2 forum that I think everyone should read.

Actually, I'm going to place this all-important sticky in the Administrative Questions category under the Other forum.

Is the log decrement method the only way to calculate damping ratio for this lab?

I ask because our data for each trial only yields one peak displacement, while this equation requires multiple peak displacements. Does this suggest that we need to re-plot our data in a program such as Matlab and find multiple peak displacements in order to calculate the damping ratio.

That's all. Thanks.

Charlie

cjrotman wrote:

Is the log decrement method the only way to calculate damping ratio for this lab?

I ask because our data for each trial only yields one peak displacement, while this equation requires multiple peak displacements. Does this suggest that we need to re-plot our data in a program such as Matlab and find multiple peak displacements in order to calculate the damping ratio.

That's all. Thanks.

Charlie

You need to do log decrement on the strain vs time curve. Use the peaks of strain to determine log decrement.

Yep, that's how to do it. You will not be using the FFT to get the damping ratio...use the time-based data.

Do any two adjacent peaks work for the log decrement method ie can you use delta=ln(xi/xi+1) for any i?

Yes, any two successive, positive peaks will do.