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 3 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. y = Hint: e^(-16t) (((1/(2sqrt(2))*e^(8sqrt(2)t)-(1/(2sqrt(2))*e^(-8sqrt(2)t))
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 3 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. y = Hint: e^(-16t) (((1/(2sqrt(2))*e^(8sqrt(2)t)-(1/(2sqrt(2))*e^(-8sqrt(2)t))
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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Transcribed Image Text: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 3 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.
y =
Hint:
e^(-16t)(((1/(2sqrt(2))*e^(8sqrt(2)t)-(1/(2sqrt(2))*e^(-8sqrt(2)t))
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