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