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## Does logarithmic decrement depend on initial amplitude?

Lets say we have a weight attached to a spring. When releasing it under water (whole motion occours under water) at different initial amplitudes, will logarithmic decrement be the same? And will the period change?

I think it should be the same for different initial amplitudes. But $\Theta=\frac{T_1}{t}\ln\frac{A_1}{A(t)}$, where $T_1$ is period of first cycle, $t$ is time until amplitude is $A(t)$ and $A_1$ is initial amplitude, suggests that when initial amplitude increases, logarithmic decrement must increase as well, or the ratio $\frac{T_1}{t}$ must decrease.

So... which one is correct?
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