A mass weighting 32 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 44 lbs when the mass has a velocity of 2 ft/sec.
A mass weighting 32 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 44 lbs when the mass has a velocity of 2 ft/sec.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Problem Statement
A mass weighing \(32 \text{ lbs}\) stretches a spring \(3 \text{ inches}\). The mass is in a medium that exerts a viscous resistance of \(44 \text{ lbs}\) when the mass has a velocity of \(2 \text{ ft/sec}\).
Suppose the object is displaced an additional \(7 \text{ inches}\) and released.
Find an equation for the object's displacement, \(u(t)\), in feet after \(t\) seconds.
\[u(t) = \]
### Explanation
This problem involves finding the displacement of a mass attached to a spring over time, considering both the spring force and a resistance force due to the medium the mass is in.
The given mass stretches the spring, and then additional displacement is applied and then released. The system is described by a differential equation that models the harmonic motion with damping.
To solve for \(u(t)\), we need to set up and solve the corresponding differential equation considering:
1. The initial displacement \(7 \text{ inches}\),
2. The viscous resistance, and
3. The spring constant.
The problem provides all necessary constants:
- Mass: \(32 \text{ lbs}\)
- Initial stretch: \(3 \text{ inches}\)
- Resistance: \(44 \text{ lbs}\) at \(2 \text{ ft/sec}\)
We'll use these to derive and solve the equation for \(u(t)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc700bc18-61e4-4e04-a31d-52f10b21c2d0%2Fc17381de-7f75-499d-92c7-50815ece71ee%2Fkj3eng_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A mass weighing \(32 \text{ lbs}\) stretches a spring \(3 \text{ inches}\). The mass is in a medium that exerts a viscous resistance of \(44 \text{ lbs}\) when the mass has a velocity of \(2 \text{ ft/sec}\).
Suppose the object is displaced an additional \(7 \text{ inches}\) and released.
Find an equation for the object's displacement, \(u(t)\), in feet after \(t\) seconds.
\[u(t) = \]
### Explanation
This problem involves finding the displacement of a mass attached to a spring over time, considering both the spring force and a resistance force due to the medium the mass is in.
The given mass stretches the spring, and then additional displacement is applied and then released. The system is described by a differential equation that models the harmonic motion with damping.
To solve for \(u(t)\), we need to set up and solve the corresponding differential equation considering:
1. The initial displacement \(7 \text{ inches}\),
2. The viscous resistance, and
3. The spring constant.
The problem provides all necessary constants:
- Mass: \(32 \text{ lbs}\)
- Initial stretch: \(3 \text{ inches}\)
- Resistance: \(44 \text{ lbs}\) at \(2 \text{ ft/sec}\)
We'll use these to derive and solve the equation for \(u(t)\).
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