A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system is then put into motion in a medium offering a damping force numerically equal to the velocity. If the mass is pulled down 6 inches from equilibrium and released, the initial value problem describing the position, x(t), of the mass at time t is x" -8x' +32x = 0, x (0) = , x' (0) = 0 6. • x" + 8x' + 32x = 0, ¤ (0) = ;, x' (0) = 0 %3D O g" + 8x' + 32x = 0, x (0) = 6, x' (0) = 0 O g" – 8x' + 32x = 0, ¤ (0) = 6, x' (0) = 0 %3D %3D

A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system is then put into motion in a medium offering a damping force numerically equal to the velocity. If the mass is pulled down 6 inches from equilibrium and released, the initial value problem describing the position, x(t), of the mass at time t is x" -8x' +32x = 0, x (0) = , x' (0) = 0 6. • x" + 8x' + 32x = 0, ¤ (0) = ;, x' (0) = 0 %3D O g" + 8x' + 32x = 0, x (0) = 6, x' (0) = 0 O g" – 8x' + 32x = 0, ¤ (0) = 6, x' (0) = 0 %3D %3D

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system
is then put into motion in a medium offering a damping force numerically equal to the
velocity. If the mass is pulled down 6 inches from equilibrium and released, the initial
value problem describing the position, x(t), of the mass at time t is
x" – 8x' + 32x = 0, x (0) =, x' (0) = 0
2
x" + 8x' + 32x = 0, x (0) = ;, x' (0) = 0
%3D
%3D
O g" + 8x' + 32x = 0, x (0) = 6, x' (0) = 0
O g" – 8x' + 32x = 0, ¤ (0) = 6, x' (0) = 0
%3D
||
-
%3D

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