Question

An undamped oscillator has period ro = 1.000 s, but I now add a little damping so that its period changes to r i = 1.001 s. What is the damping factor 8? By what factor will the amplitude of oscillation decrease after 10 cycles? Which effect of damping would be more noticeable, the change of period or the decrease of the amplitude?

Answer 1

The damping factor of the oscillator is 0.001. The decrease in amplitude after 10 cycles can be calculated using the formula Decrease in Amplitude = (Amplitude) * (1 - Damping Factor)^10. The effect of damping that would be more noticeable depends on the specific situation.

Step-by-step explanation:

The damping factor of an oscillator can be determined by the equation:

Damping Factor = (Change in Period) / (Original Period)

In this case, the change in period is given as 1.001 s - 1.000 s = 0.001 s. The original period is 1.000 s. Therefore, the damping factor is 0.001.

The decrease in amplitude after 10 cycles can be calculated using the formula:

Decrease in Amplitude = (Amplitude) * (1 - Damping Factor)^10

The effect of damping that would be more noticeable depends on the specific situation. If the change in period is significant, then the change in period would be more noticeable. If the decrease in amplitude is significant, then the decrease in amplitude would be more noticeable.