The amplitude of a damped harmonic oscillator becomes
\[
\frac{1}{2\sqrt2}
\]
times its initial amplitude in a time of \(6\) s. Additional time taken for the amplitude to become
\[
\frac{1}{4\sqrt2}
\]
times its initial amplitude is
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In damped oscillations,
\[
\boxed{A=A_0e^{-kt}.}
\]
Take the ratio of amplitudes at different times to eliminate the initial amplitude and determine the required time interval.