Alternating Current

JEE Main level, single correct, medium

150 of 190

Question 150 of 190

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 :

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Answer: (A) 0.729

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(15\right)}{2\text{m}}} ...... (ii)

From (i) and (ii)

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

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