Answer:
[tex]A=\frac{A_0}{\sqrt 3}[/tex]
Explanation:
Initial amplitude=[tex]A_0[/tex]
We are given that
Amplitude after 2 s=A=[tex]\frac{1}{3}A_0[/tex]
We have to find the amplitude after 1 s.
We know that amplitude at any time t
[tex]A=A_0e^{-\alpha t}[/tex]
Using the formula
[tex]\frac{A_0}{3}=A_0e^{-2\alpha}[/tex]
[tex]\frac{1}{3}=e^{-2\alpha}[/tex]
[tex]3=e^{2\alpha}[/tex]
[tex]ln 3=2\alpha[/tex]
[tex]\alpha =\frac{ln 3}{2}=ln\sqrt 3[/tex]
[tex]e^{\alpha}=\sqrt 3}[/tex]
When t=1 s
[tex]A=A_0e^{-\alpha}=\frac{A_0}{\sqrt 3}[/tex]
