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Question

Physics Question on Oscillations

When an oscillator completes 100100 oscillations its amplitude reduced to 13\frac{1}{3} of initial value. What will be its amplitude, when it completes 200200 oscillations?

A

18\frac{1}{8}

B

23\frac{2}{3}

C

16\frac{1}{6}

D

19\frac{1}{9}

Answer

19\frac{1}{9}

Explanation

Solution

For damped oscillation amplitude A=A0e−btA = A _{0} e ^{- b t}
A03=A0e−b(100T)⇒e−100bT=13\frac{ A _{0}}{3}= A _{0} e ^{- b (100 T )} \Rightarrow e ^{-100 bT }=\frac{1}{3}
at t=200T,A=A0e−b(200T)=A0(e−100bT)2t =200 T , A = A _{0} e ^{- b (200 T )}= A _{0}\left( e ^{-100 b T }\right)^{2}
⇒A=A0(13)2\Rightarrow A = A _{0}\left(\frac{1}{3}\right)^{2}
=A09=\frac{ A _{0}}{9}