Learnwith MYLARU INFRA

Structural dynamics · logarithmic decrement

Measuring Damping from Response

Estimate damping from observed decay and response records.

Approx. 32 min

Learning objectives

By the end of this lesson

  • Define logarithmic decrement in physical engineering terms.
  • Use logarithmic decrement with consistent quantities and units.
  • Change model inputs and explain the resulting trend.
  • Separate an educational model result from a code-based safety decision.

Before you calculate

What this means in the real world

01

What the formula is for

Peak measurements from a free-decay trace provide an experimental route to damping estimation.

δ = (1/n) ln(x₀/xₙ)
02

Where an engineer uses it

Ambient vibration test of a floor: This application turns logarithmic decrement into a real modelling decision.

Extract clean same-direction peaks from a measured acceleration or displacement record.

03

What a wrong value can do

A wrong unit, sign, scale, boundary condition, or property can produce a believable number with the wrong physical meaning. It may understate demand, exaggerate it, or lead to the wrong failure check.

Definition

logarithmic decrement

The natural logarithm of the ratio between response peaks separated by a chosen number of cycles.

Why it mattersIt provides the central modelling idea for measuring damping from response and connects observed motion to a solvable engineering representation.

Build the physical picture

Estimate damping from observed decay and response records. Start by identifying the system boundary, response coordinates, applied action, and the properties that store or dissipate energy. A useful model is the simplest one that preserves the behaviour needed for the engineering question.

Formula

Logarithmic decrement

δ = (1/n) ln(x₀/xₙ)

Peak measurements from a free-decay trace provide an experimental route to damping estimation.

u
response displacement or displacement vectorm
t
times
ω
angular frequency where usedrad/s

Interactive concept

Explore logarithmic decrement

Change the available model inputs, watch the motion or force relationship, and describe the trend before reading the numerical result.

How is the load applied?
How does the structure behave?
LoadTime →
Load⇣
Lower dynamic tendency

A gradual action on a relatively rigid structure is more likely to remain close to static behaviour.

04

Real-world application

Ambient vibration test of a floor

This application turns logarithmic decrement into a real modelling decision.

Modelling move
Extract clean same-direction peaks from a measured acceleration or displacement record.
Engineering question
Is the observed decay consistent enough to justify one equivalent damping ratio?

Calculate, compare, interpret

Editable formula question

Convert period into frequency: Measuring Damping from Response

Select an oscillator period and calculate its cyclic natural frequency.

fₙ = 1/Tₙ
Substitute your current valuesfₙ = 1 ÷ 1Answer format: enter the numerical result only in Hz. Example: 12, not “answer = 12”.
Hz
Round only at the final step. The accepted tolerance for this exercise is ±0.01.

The displayed minimum, maximum, and textbook values define this learning exercise only. They are not universal design limits.

Editable formula question

Compare a model demand with your entered criterion

Enter a demand and a comparison value chosen for this exercise, then interpret the ratio.

utilization indicator = model demand / entered criterion
Substitute your current valuesratio = 4 ÷ 5Answer format: enter the numerical result only (no unit for this dimensionless result). Example: 12, not “answer = 12”.
—
Round only at the final step. The accepted tolerance for this exercise is ±0.01.

The displayed minimum, maximum, and textbook values define this learning exercise only. They are not universal design limits.