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EEJ MAIN Physics QUESTION #7077
Question 1
A damped oscillator's amplitude reduces to $0.9$ times its starting value over $5$ seconds. Determine the factor $a$ by which the amplitude will have decreased relative to the original magnitude after an additional $10$ seconds.
  • $0.7$
  • $0.81$
  • $0.729$✔️
  • $0.6$
Correct Answer Explanation
In damping, the amplitude follows $A = A_0 e^{-\gamma t}$. In $5\text{s}$, $A_1 = 0.9 A_0$. After a total of $15\text{s}$ ($5\text{s} + 10\text{s}$), the time is three times the initial interval. Thus, the amplitude becomes $A_2 = A_0 (0.9)^3 = 0.729 A_0$. The factor $a$ is $0.729$.