A damped oscillator is released from rest with an initial displacement of 10.00 cm. At the end of the first complete oscillation, the displa

Question

A damped oscillator is released from rest with an initial displacement of 10.00 cm. At the end of the first complete oscillation, the displacement reaches 9.05 cm. When 4 more oscillations are completed, what is the displacement reached

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Kim Chi 5 months 2021-08-09T15:16:50+00:00 1 Answers 20 views 0

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    2021-08-09T15:18:36+00:00

    Answer:

    The  displacement is  A_r =  6.071 \ cm

    Explanation:

    From the question we are told that

       The initial displacement is A_o  =  10 \ cm

         The displacement at the end of first oscillation is  A_d  = 9.05 \ cm

         

    Generally the damping constant of this damped oscillator is mathematically represented as  

               \eta  =  \frac{A_d}{A_o}

    substituting values

               \eta  =  \frac{9.05}{10}

            \eta  =  0.905

    The displacement after 4 more oscillation is mathematically represented as

           A_r =  \eta^4 *  A_d

    substituting values

          A_r =  (0.905)^4 *   (9.05)

          A_r =  6.071 \ cm

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