A) \[\frac{1}{30}\ln 3\]
B) \[\frac{1}{15}\ln 3\]
C) 2
D) \[\frac{1}{2}\]
Correct Answer: A
Solution :
Amplitude in a damped oscillation is given by \[A={{A}_{0}}{{e}^{-\beta t}}\] energy \[\propto {{A}^{2}}\] \[\therefore \] \[\sqrt{E}=\sqrt{{{E}_{0}}}{{e}^{-\beta t}}\] where \[{{E}_{0}}\] is initial energy \[\sqrt{15}=\sqrt{45}{{e}^{-\beta 15\sec }}\] \[{{3}^{\frac{1}{2}}}={{e}^{-15\beta }}\] on taking log both sides \[-\frac{1}{2}\ln \left( 3 \right)=-15\beta \] \[\beta =\frac{\ln 3}{30}=4\]
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