A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 7 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that aftert seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second.
A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 7 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that aftert seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Problem Description:**
A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring \( \frac{1}{2} \) feet. The ball is started in motion from the equilibrium position with a downward velocity of 7 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second).
Suppose that after \( t \) seconds the ball is \( y \) feet below its rest position. Find \( y \) in terms of \( t \). (Note that the positive direction is down.)
Take as the gravitational acceleration 32 feet per second per second.
**Equation:**
\[ y = \]
*Provide your answer or continue working through calculations to find \( y \) in terms of \( t \).*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56661073-d5cb-4d6d-af43-dff77ec9898b%2F5fcdff4d-cf1e-43fb-a394-4c471d1fa5a7%2Fh9rubjq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring \( \frac{1}{2} \) feet. The ball is started in motion from the equilibrium position with a downward velocity of 7 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second).
Suppose that after \( t \) seconds the ball is \( y \) feet below its rest position. Find \( y \) in terms of \( t \). (Note that the positive direction is down.)
Take as the gravitational acceleration 32 feet per second per second.
**Equation:**
\[ y = \]
*Provide your answer or continue working through calculations to find \( y \) in terms of \( t \).*
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