F ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation Evaluate the surface integral F(x, y, z) xy i 12x2 j+yz k S is the surface z xe, 0 sxs 1,0 sys 2, with upward orientation A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) ft
F ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation Evaluate the surface integral F(x, y, z) xy i 12x2 j+yz k S is the surface z xe, 0 sxs 1,0 sys 2, with upward orientation A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) 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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Transcribed Image Text:F ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation
Evaluate the surface integral
F(x, y, z) xy i 12x2 j+yz k
S is the surface z xe, 0 sxs 1,0 sys 2, with upward orientation
Transcribed Image Text:A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is
then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity.
(a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the
equilibrium position.
x(t)
ft
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