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Change in Period or Amplitude of an Undamped Oscillator

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An undamped oscillator has a period t_o = 1.000 s, but I now add a little damping so that its period changes to t_1 = 1.001 s. What is the damping factor B? By what factor will the amplitude of oscillation decrease after 10 cycles? What effect of damping would be more noticeable, the change of period or the decrease of amplitude?

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