In the picture above, the logarithmic decrement is defined and explained. I can't make out the meaning.
I tried searching on Google but it didn't help. Can you explain it in a simple yet effective way?
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I have attached an image of a sinusoidal damped oscillation that shows the two amplitudes of which ratio $x = B_1 C_1 / B_2 C_2$ (which is $x_1 / x_2$ in the question) is measured
Here, $$ x = e^\lambda = \frac{B_1C_1}{B_2C_2} = \frac{B_2C_2}{B_3C_3} $$
and $x$ is what is named decrement.
In order to usually find the viscosity of the medium in which a pendulum oscillates and it's amplitude studied (or any other purpose), we define a term called logarithmic decrement, $λ$ that is numerically equal to $\log(x)$.
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$\begingroup$ Is it not the ratio of amplitudes separated by one period of the oscillations rather than half a period? $\endgroup$– FarcherCommented Dec 10, 2017 at 12:06
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$\begingroup$ A very common doubt, actually, here it is the ratio of amplitudes separated by half period only and not one. As in the question, we see that in eqn. 2.19 the term bT is divided by 2 in order to account for that. If the ratio were taken in one oscillation, the '2' would not be there. $\endgroup$– sonuCommented Dec 10, 2017 at 12:15
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1$\begingroup$ Note that you can (and should) use LaTeX notation for typesetting mathematics. For a tutorial, see here. $\endgroup$ Commented Dec 10, 2017 at 16:18