A 1 kilogram mass is attached to a spring hanging vertically from a ceiling. At time t = 0, the mass passes through the equilibrium position with a velocity 10cm/s moving downwards. Model the spring position y(t) as a function of time by the equation my" -ky-yY'. The spring constant is k = 1N/m, the friction coefficient y is not known. (a) State the initial value problem describing the mass's motion. (b) Solve the initial problem formulated in (a), assuming that there is no friction. (c) Still assuming that there is no friction, what is the period T of the motion? (d) In an experiment it was observed that the period is 47 seconds, what is the value of y consistent with that observation? =
A 1 kilogram mass is attached to a spring hanging vertically from a ceiling. At time t = 0, the mass passes through the equilibrium position with a velocity 10cm/s moving downwards. Model the spring position y(t) as a function of time by the equation my" -ky-yY'. The spring constant is k = 1N/m, the friction coefficient y is not known. (a) State the initial value problem describing the mass's motion. (b) Solve the initial problem formulated in (a), assuming that there is no friction. (c) Still assuming that there is no friction, what is the period T of the motion? (d) In an experiment it was observed that the period is 47 seconds, what is the value of y consistent with that observation? =
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 1 kilogram mass is attached to a spring hanging vertically from a ceiling. At time \( t = 0 \), the mass passes through the equilibrium position with a velocity \( 10 \text{cm/s} \) moving downwards. Model the spring position \( y(t) \) as a function of time by the equation
\[ my'' = -ky - \gamma y'. \]
The spring constant is \( k = 1 \text{N/m} \), the friction coefficient \( \gamma \) is not known.
(a) State the initial value problem describing the mass’s motion.
(b) Solve the initial problem formulated in (a), assuming that there is no friction.
(c) Still assuming that there is no friction, what is the period \( T \) of the motion?
(d) In an experiment it was observed that the period is \( 4\pi \) seconds, what is the value of \( \gamma \) consistent with that observation?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeefd442-7c64-4a51-8ed1-c0196ac6a13e%2F6e10d1c2-c044-48a6-8df6-d9ca35ad9e24%2Ffxtz16s_processed.png&w=3840&q=75)
Transcribed Image Text:A 1 kilogram mass is attached to a spring hanging vertically from a ceiling. At time \( t = 0 \), the mass passes through the equilibrium position with a velocity \( 10 \text{cm/s} \) moving downwards. Model the spring position \( y(t) \) as a function of time by the equation
\[ my'' = -ky - \gamma y'. \]
The spring constant is \( k = 1 \text{N/m} \), the friction coefficient \( \gamma \) is not known.
(a) State the initial value problem describing the mass’s motion.
(b) Solve the initial problem formulated in (a), assuming that there is no friction.
(c) Still assuming that there is no friction, what is the period \( T \) of the motion?
(d) In an experiment it was observed that the period is \( 4\pi \) seconds, what is the value of \( \gamma \) consistent with that observation?
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