Новое решение
en/3.5.39.md
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| + | ### Statement | ||
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| + | $3.5.39.$ [Insert the problem statement] | ||
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| + | ### Solution | ||
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| + | From $Q=10^9$ and $\omega_0=10^4$ s$^{-1}$, we have $\gamma=\omega_0/(2Q)=5\times10^{-6}$ s$^{-1}$. The amplitude of the transient response decays according to the exponential $e^{-\gamma t}$, which becomes less than $5\%$ for $t\approx3/\gamma$. Thus the forced oscillation is firmly established after roughly $6\times10^5$ s. An order-of-magnitude estimate is $\sim10^5-10^6$ s. | ||
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| + | #### Answer | ||
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| + | [Insert a concise answer or boxed result] | ||
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| ### Statement | |||
| $3.5.39.$ [Insert the problem statement] | |||
| ### Solution | |||
| From $Q=10^9$ and $\omega_0=10^4$ s$^{-1}$, we have $\gamma=\omega_0/(2Q)=5\times10^{-6}$ s$^{-1}$. The amplitude of the transient response decays according to the exponential $e^{-\gamma t}$, which becomes less than $5\%$ for $t\approx3/\gamma$. Thus the forced oscillation is firmly established after roughly $6\times10^5$ s. An order-of-magnitude estimate is $\sim10^5-10^6$ s. | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||