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

Answer 1

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

      $A_r = (0.905)^4 * (9.05)$

      $A_r = 6.071 \ cm$