Question

I am currently doing my oscillation homework and I am stuck on a dampening question. The question is in the attachment below.
Thank you for your time.

Answer 1

The amplitude A(t) of a damped oscillator are related to time by the subsequent relationship:
\[A(t)=A _{0}*e ^{-\gamma t/2}\]
where A_0 is the initial amplitude, namely A_0=A(t=0).
Now, from the text of your problem I can write:
\[A _{0}e ^{-\gamma t ^{*}/2}=\frac{ A _{0} }{ 100 }\]
where t^* is the time at which the amplitude is became 1/100 of the initial amplitude.
So, we can write:
\[e ^{y t ^{*}/2}=\frac{ 1 }{ 100 }\]
and finally:
\[\gamma=\frac{ 4*\ln 10 }{ 8.36 }\approx 1.1 \sec ^{-1}\]

Answer 2

oops! I have made an error:
\[e ^{-\gamma t ^{*}/2}=\frac{ 1 }{ 100 }\]
and finally...

Answer 3

Thank you for your response. I am a bit lost though. Do I plug in my 1.1 to the last equation?