A spring with a 5-kg mass and a damping constant 15 can be held stretched 2 meters beyond its natural length by a force of 8 newtons. Suppose the spring is stretched 4 meters beyond its natural length and then released with zero velocity. In the notation of the text, what is the value c² - 4mk? m²kg²/sec² Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t of the form c₁eat + c₂eßt where (the larger of the two) (the smaller of the two) α = B = C1 = C₂ =
A spring with a 5-kg mass and a damping constant 15 can be held stretched 2 meters beyond its natural length by a force of 8 newtons. Suppose the spring is stretched 4 meters beyond its natural length and then released with zero velocity. In the notation of the text, what is the value c² - 4mk? m²kg²/sec² Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t of the form c₁eat + c₂eßt where (the larger of the two) (the smaller of the two) α = B = C1 = C₂ =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![A spring with a 5-kg mass and a damping constant 15 can be held stretched 2 meters beyond its natural length by a force of 8 newtons. Suppose the spring is stretched 4 meters beyond its natural length and then released with zero velocity. In the notation of the text, what is the value \( c^2 - 4mk \)?
\[ \boxed{\phantom{\text{}}} \]
Find the position of the mass, in meters, after \( t \) seconds. Your answer should be a function of the variable \( t \) of the form \( c_1 e^{\alpha t} + c_2 e^{\beta t} \) where
\[
\begin{align*}
\alpha &= \phantom{\text{(the larger of the two)}} \\
\beta &= \phantom{\text{(the smaller of the two)}} \\
c_1 &= \phantom{\text{}} \\
c_2 &= \phantom{\text{}}
\end{align*}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f1c68a1-c113-41cc-b0cf-42f2666e5687%2F9047b218-ae5a-459c-8357-2a507e941485%2Fkkl3a84_processed.png&w=3840&q=75)
Transcribed Image Text:A spring with a 5-kg mass and a damping constant 15 can be held stretched 2 meters beyond its natural length by a force of 8 newtons. Suppose the spring is stretched 4 meters beyond its natural length and then released with zero velocity. In the notation of the text, what is the value \( c^2 - 4mk \)?
\[ \boxed{\phantom{\text{}}} \]
Find the position of the mass, in meters, after \( t \) seconds. Your answer should be a function of the variable \( t \) of the form \( c_1 e^{\alpha t} + c_2 e^{\beta t} \) where
\[
\begin{align*}
\alpha &= \phantom{\text{(the larger of the two)}} \\
\beta &= \phantom{\text{(the smaller of the two)}} \\
c_1 &= \phantom{\text{}} \\
c_2 &= \phantom{\text{}}
\end{align*}
\]
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