(b) State the initial value problem describing the mass's motion upon starting from its release, Solution: Displacement y from equilibrium solves the equation given in the lecture y" : = k m y = -500y, the initial values given in the problem are y(0) = 0 and y'(0) = 0.01.
(b) State the initial value problem describing the mass's motion upon starting from its release, Solution: Displacement y from equilibrium solves the equation given in the lecture y" : = k m y = -500y, the initial values given in the problem are y(0) = 0 and y'(0) = 0.01.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Can you explain step by step how they got the answer to part B
![Problem 2: A 100 gram mass, when attached to a spring hanging vertically, stretches the spring
2cm. The mass is then released from the equilibrium position with an initial velocity 1cm/s.
Assume that there is no dumping.
(a) Determine the spring constant k,
Solution: Equating the gravitational force and spring force I get
50Nm-¹.
k =
mg 10 × 0.1
0.02
Ax
=
(b) State the initial value problem describing the mass's motion upon starting from its release,
Solution: Displacement y from equilibrium solves the equation given in the lecture
k
-y = -500y,
m
the initial values given in the problem are y(0) = 0 and y'(0) = 0.01.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeefd442-7c64-4a51-8ed1-c0196ac6a13e%2Fd125fa10-a602-498c-8e45-b784c211392e%2F3pmwc5b_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2: A 100 gram mass, when attached to a spring hanging vertically, stretches the spring
2cm. The mass is then released from the equilibrium position with an initial velocity 1cm/s.
Assume that there is no dumping.
(a) Determine the spring constant k,
Solution: Equating the gravitational force and spring force I get
50Nm-¹.
k =
mg 10 × 0.1
0.02
Ax
=
(b) State the initial value problem describing the mass's motion upon starting from its release,
Solution: Displacement y from equilibrium solves the equation given in the lecture
k
-y = -500y,
m
the initial values given in the problem are y(0) = 0 and y'(0) = 0.01.
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