A mass weighing 4 pounds stretches a spring 6 inches. The mass is initially released from a point 2 inches below the equilibrium position with an upward velocity of 8 ft/s. Assume the spring/mass system has free undamped motion. a. Find the spring constant k. b. Find xo in the initial condition x(0) = xo.. Find in the initial condition x'(0) = x1. с. X1 d. The differential equation in normal form for the equation of motion has the d?x form "+ w2x = 0. Find the value of w?. dt2
A mass weighing 4 pounds stretches a spring 6 inches. The mass is initially released from a point 2 inches below the equilibrium position with an upward velocity of 8 ft/s. Assume the spring/mass system has free undamped motion. a. Find the spring constant k. b. Find xo in the initial condition x(0) = xo.. Find in the initial condition x'(0) = x1. с. X1 d. The differential equation in normal form for the equation of motion has the d?x form "+ w2x = 0. Find the value of w?. dt2
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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Question
1
![A mass weighing 4 pounds stretches a spring 6 inches. The mass is initially
released from a point 2 inches below the equilibrium position with an upward
velocity of 8 ft/s. Assume the spring/mass system has free undamped motion.
1.
а.
Find the spring constant k.
b. Find xo in the initial condition x(0) = x..
Find
in the initial condition x'(0) = x1.
с.
X1
d. The differential equation in normal form for the equation of motion has the
d²x
form "+ w²x = 0. Find the value of w².
dt2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd936c6c0-8e3b-4a92-9646-2c460fec57ae%2F97ad62c3-1378-4816-9d17-12d35297f579%2Fdqpu7n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A mass weighing 4 pounds stretches a spring 6 inches. The mass is initially
released from a point 2 inches below the equilibrium position with an upward
velocity of 8 ft/s. Assume the spring/mass system has free undamped motion.
1.
а.
Find the spring constant k.
b. Find xo in the initial condition x(0) = x..
Find
in the initial condition x'(0) = x1.
с.
X1
d. The differential equation in normal form for the equation of motion has the
d²x
form "+ w²x = 0. Find the value of w².
dt2
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