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JEE Main 20137 April
Exam
JEE Main
Year
2013
Date
7 April
Subject
Physics
Chapter
Alternating Current

JEE Main 2013 · 7 April · Physics · Alternating Current

The amplitude of a damped oscillator decreases to 0.9 times its...

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to α\alpha times its original magnitude, where α\alpha equals :

Options

  1. A0.729
  2. B0.6
  3. C0.7
  4. D0.81

Correct answer

A. 0.729

Step-by-step solution

A=A0e−bt2m\text{A} = {\text{A}}_{0}{\text{e}}^{- \dfrac{\text{bt}}{2\text{m}}}

After 5 second

0.9A0=A0e−b(5)2m\text{0.9} {\text{A}}_{0} = {\text{A}}_{0} {\text{e}}^{- \dfrac{\text{b} \left(5\right)}{2 \text{m}}} ...... (i)

After 10 more second

A=A0e−b(15)2m\text{A} = {\text{A}}_{0} {\text{e}}^{- \dfrac{\text{b} \left(1 5\right)}{2 \text{m}}} ...... (ii)

From (i) and (ii)

A=0.729 A0\text{A} = {\text{0.729 A}}_{0}
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