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? 145 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 α = (-15+sqrt145)/10 (the larger of the two) B= (-15-sqrt145)/10 (the smaller of the two) C1 = 15(sqrt145)+145 C₂ -143+15(sqrt145)
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? 145 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 α = (-15+sqrt145)/10 (the larger of the two) B= (-15-sqrt145)/10 (the smaller of the two) C1 = 15(sqrt145)+145 C₂ -143+15(sqrt145)
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Please find the correct answer for c1 and c2. The answer is wrong even if I switch the two.
![A spring with a 5-kg mass and a damping constant of 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 \( c^2 - 4mk \)?
\[ 145 \]
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:
\[
\alpha = \frac{-15 + \sqrt{145}}{10} \quad (\text{the larger of the two})
\]
\[
\beta = \frac{-15 - \sqrt{145}}{10} \quad (\text{the smaller of the two})
\]
\[
c_1 = 15(\sqrt{145}) + 145
\]
\[
c_2 = -143 + 15(\sqrt{145})
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f1c68a1-c113-41cc-b0cf-42f2666e5687%2F6a9fed48-d2a8-4792-9d51-06329639e879%2Fwihurkj_processed.png&w=3840&q=75)
Transcribed Image Text:A spring with a 5-kg mass and a damping constant of 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 \( c^2 - 4mk \)?
\[ 145 \]
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:
\[
\alpha = \frac{-15 + \sqrt{145}}{10} \quad (\text{the larger of the two})
\]
\[
\beta = \frac{-15 - \sqrt{145}}{10} \quad (\text{the smaller of the two})
\]
\[
c_1 = 15(\sqrt{145}) + 145
\]
\[
c_2 = -143 + 15(\sqrt{145})
\]
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