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en/3.5.38.md
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| + | ### Statement | ||
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| + | $3.5.38.$ [Insert the problem statement] | ||
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| + | ### Solution | ||
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| + |  | ||
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| + | The energy (and hence the square of the amplitude of the velocity) of a weakly-damped forced oscillator, where $\gamma\ll\omega_0$, near resonance is proportional to | ||
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| + | \[\frac{1}{(\omega-\omega_0)^2+\gamma^2}.\] | ||
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| + | This means that the resonance curve peaks at $\omega=\omega_0$ and the width of the curve at half of the maximum height is $2\gamma$. Reading from the provided graph, we have $\omega_0\approx540$ s$^{-1}$ and $\gamma\approx60$ s$^{-1}$, and the quality factor is $Q=\omega_0/(2\gamma)\approx4.5$. | ||
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| + | #### Answer | ||
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| + | [Insert a concise answer or boxed result] | ||
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| ### Statement | |||
| $3.5.38.$ [Insert the problem statement] | |||
| ### Solution | |||
|  | |||
| The energy (and hence the square of the amplitude of the velocity) of a weakly-damped forced oscillator, where $\gamma\ll\omega_0$, near resonance is proportional to | |||
| \[\frac{1}{(\omega-\omega_0)^2+\gamma^2}.\] | |||
| This means that the resonance curve peaks at $\omega=\omega_0$ and the width of the curve at half of the maximum height is $2\gamma$. Reading from the provided graph, we have $\omega_0\approx540$ s$^{-1}$ and $\gamma\approx60$ s$^{-1}$, and the quality factor is $Q=\omega_0/(2\gamma)\approx4.5$. | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||