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qid 8636 · math

Question: A mass weighing $8 \mathrm{lb}$ stretches a spring 1.5 in. The mass is also attached to a damper with coefficient $\gamma$. Determine the value of $\gamma$ for which the system is critically damped; be sure to give the units for $\gamma$

  1. 10 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$
  2. 2 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$
  3. 4 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$
  4. 14 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$
  5. 6 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$
  6. 20 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$
  7. 16 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$
  8. 18 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$
  9. 12 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$
  10. 8 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$

Our answer: J. 8 $\mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}$ Source quote machine-checked (exact quote)

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How it was answered

Multi-step solver (maze), replayed by code

card: maze · card sha256 16e68837dca3214d…

Current source

LibreTexts Mathematics, Differential Equations (MTH 225), 6.2 "Spring Problems II"

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/06:_Applications_of_Linear_Second_Order_Equations/6.02:_Spring_Problems_II

“We say the motion is critically damped if”

Source quote machine-checked (exact quote)

retrieved 2026-09-18T00:09:37.607Z

page text sha256 14ccc7eb82ff02fc… · content sha256 aaa6c1d2cefa7664…

addendum maze_qid8636_b4_maze_input_ADDENDUM_source_rs20260918T000937Z · sha256 df761abf7e397b4a… · replaces the version below, addendum sha256 3e114bf9a76a1f7e…

Earlier version (superseded)

https://openstax.org/books/university-physics-volume-1/pages/15-5-damped-oscillations

Source weak (http_get_200_text_and_question_terms)

retrieved 2026-09-17T23:24:55.052Z

page text sha256 16673b3c56489c96… · content sha256

addendum maze_qid8636_b4_maze_input_ADDENDUM_source_bf20260917T232455Z · sha256 3e114bf9a76a1f7e… · replaces the version below, addendum sha256 22f9e8e844e75c1b…

Earlier version (superseded)

No public source has been found for this card yet (3 places checked internally).

addendum maze_qid8636_b4_maze_input_ADDENDUM_source · sha256 22f9e8e844e75c1b…

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