The energy of an oscillator decreases by 3% each cycle.The quality factor of this oscillator is approximately
A)209
B)157
C)87
D)63
E)21

Question

Quizplus · Accepted Answer

The quality factor (Q) of an oscillator is given by the formula Q = π / (energy loss per cycle / energy stored per cycle). If the energy decreases by 3% each cycle, the energy loss per cycle is 0.03 times the energy stored. Therefore, Q = π / 0.03 ≈ 104.72. However, this calculation seems to have been misunderstood. The correct approach to find the quality factor related to energy decay in an oscillator involves understanding that the quality factor is also related to the decay of amplitude or energy over time. Given the 3% energy loss per cycle, a more accurate approach involves relating this loss to the exponential decay factor over one period, leading to a different interpretation of the quality factor. The discrepancy in the initial explanation suggests a mistake in the calculation or interpretation. The correct calculation should involve understanding the relationship between the energy loss and the exponential decay over time, which can be related to the quality factor through more complex formulas involving the logarithmic decrement or the fractional energy loss per cycle.

The Energy of an Oscillator Decreases by 3% Each Cycle