A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 8 inches above the equilibrium position. Find the equation of motion (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = X ft
A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 8 inches above the equilibrium position. Find the equation of motion (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = X ft
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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Please helpm with these problems. i can't get the right answer for some of them.
![A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 8 inches above the equilibrium position. Find the equation of motion. (Use \( g = 32 \, \text{ft/s}^2 \) for the acceleration due to gravity.)
\[ x(t) = \boxed{} \, \text{ft} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6589b73f-c70a-44b7-9b99-e4dd330855a5%2F13edf5ee-8b76-4028-833d-8dc303e26c03%2Feqs6ip_processed.png&w=3840&q=75)
Transcribed Image Text:A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 8 inches above the equilibrium position. Find the equation of motion. (Use \( g = 32 \, \text{ft/s}^2 \) for the acceleration due to gravity.)
\[ x(t) = \boxed{} \, \text{ft} \]
![A mass weighing 32 pounds stretches a spring 2 feet. Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 5 ft/s.
- **Amplitude:** [Blank Input] ft (Incorrect)
- **Period:** \(\frac{\pi}{2}\) s (Correct)
How many complete cycles will the mass have completed at the end of \(6\pi\) seconds?
- **12** cycles (Correct)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6589b73f-c70a-44b7-9b99-e4dd330855a5%2F13edf5ee-8b76-4028-833d-8dc303e26c03%2F4n7wxn_processed.png&w=3840&q=75)
Transcribed Image Text:A mass weighing 32 pounds stretches a spring 2 feet. Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 5 ft/s.
- **Amplitude:** [Blank Input] ft (Incorrect)
- **Period:** \(\frac{\pi}{2}\) s (Correct)
How many complete cycles will the mass have completed at the end of \(6\pi\) seconds?
- **12** cycles (Correct)
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