When an oscillator completes 100 oscillations its amplitude reduced to 1/3 of initial value. What will be its amplitude, When it completes 200 oscillations?

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Solution

$For damped oscillation, amplitude is given by, A = A_{0} e^{- bt} where, A_{0} = Initial amplitude b = Damping constant According to question, \frac{A_{0}}{3} = A_{0} e^{- b (100 T)} or e^{- b (100 T)} = \frac{1}{3} Now, at t = 200 T A = A_{0} e^{- b (200 T)} = A_{0} [e^{- b (100 T)}]^{2} or A = A_{0} (\frac{1}{3})^{2} = \frac{A_{0}}{9}$

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When an oscillator completes 100 oscillations its amplitude reduced to 1/3 of initial value. What will be its amplitude, When it completes 200 oscillations?

For damped oscillation, amplitude is given by,A=A0e-btwhere,A0=Initial amplitudeb=Damping constantAccording to question,A03=A0e-b(100 T)or e-b(100 T)=13Now,at t=200 TA=A0e-b(200 T)=A0 [e-b(100 T)]2or A=A0(13)2=A09