A small earthquake starts a lamppost vibrating back and forth. The amplitude of
ID: 1984893 • Letter: A
Question
A small earthquake starts a lamppost vibrating back and forth. The amplitude of the vibration of the top of the lamppost is 6.1cm at the moment the quake stops, and 7.8s later it is 1.7cm.What is the time constant for the damping of the oscillation?
I have the formula that I think I'm supposed to use [Xmax=Ae^(-t/T)], but I'm not sure which numbers go to which variables. Also, I know that you are not supposed to post more than one question in a post, but there is a second part to this question that I'm not sure how to separate:
What was the amplitude of the oscillation 3.9 after the quake stopped?
If you're only able to answer that first one, that's totally fine. If possible though, answering the second one would be great.Thank you.
Explanation / Answer
Similar problem with diff values please rate we know A= Ao e -bt given Ao = 6 cm A= 1.9 cm t = 7.2 s -bt = ln ( A / Ao) = -1.1499 damping constant b = 1.1499 / t = 0.1597 s^-1 time constant T = 1/ b = 6.26 s (b). amplitude after 3.6 s is A ' = 6 e-b*3.6 = 6 e -0.1597 * 3.6 = 3.376 cm