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MMLU-Pro / 9748 / Consider a damped harmonic oscillator. After four cycles the amplitude of the…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e1 / e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.
Plain-text mathematical notation (without MathML)
Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.
Original LaTeX notation
Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to $1 / e$ of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.

category

physics

options

  1. $\frac{4 \pi}{\sqrt{16 \pi^2+1}}$
  2. $\frac{2 \pi}{\sqrt{4 \pi^2+1}}$
  3. $\frac{12 \pi}{\sqrt{144 \pi^2+1}}$
  4. $\frac{5 \pi}{\sqrt{25 \pi^2+1}}$
  5. $\frac{10 \pi}{\sqrt{100 \pi^2+1}}$
  6. $\frac{6 \pi}{\sqrt{36 \pi^2+1}}$
  7. $\frac{9 \pi}{\sqrt{81 \pi^2+1}}$
  8. $\frac{7 \pi}{\sqrt{49 \pi^2+1}}$
  9. $\frac{8 \pi}{\sqrt{64 \pi^2+1}}$

src

scibench-class

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Source and history

upstream_id / Original problem ID
9748
task_id
002e8593-cb18-55b4-a40c-157f7fce63ab
task_key
default--test--9748
task_revision_id
1
config / split
default / test

Official source

initial import