Logarithmic
decrement is a way to determine the damping ratio of an underdamped system
given the displacement response over time. Recalling that damping of a system
is not numerically solvable, this method helps us to calculate it based on the
experimental result.
First, we
derive the logarithmic decrement solution from the displacement solution. As a
result, we obtain two solutions, namely exact and approximate. Approximate
solution may be used when the damping ratio is less than 30%, else the result
will be having significant error from the actual result. Next, we implemented
the solution to solve for an example.
The following shows the application of logarithmic decrement for a damped SDOF system. Watch the video above for full details.
Derivation for solution 1
Derivation for solution 2
Derivation for solution 3
Derivation for solution 4
Derivation for solution 5
Condition for approximate solution to be valid
Example overview
Solution 1
Solution 2
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