A mass of 1 slug is attached to a spring whose constant is 5 Ib/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 7 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. (a) Assume the mass is driven by an external force equal to f(t) = 16 cos(2t) + 4 sin(2t). Find the initial conditions. x(0) = ft x'(0) = ft/s Find the particular solution. Xp = ft Find the equation of motion of the mass. x(t) = ft
A mass of 1 slug is attached to a spring whose constant is 5 Ib/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 7 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. (a) Assume the mass is driven by an external force equal to f(t) = 16 cos(2t) + 4 sin(2t). Find the initial conditions. x(0) = ft x'(0) = ft/s Find the particular solution. Xp = ft Find the equation of motion of the mass. 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:A mass of 1 slug is attached to a spring whose constant is 5 Ib/ft. Initially, the mass is released 1 foot below the equilibrium position with a
downward velocity of 7 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to
2 times the instantaneous velocity.
(a) Assume the mass is driven by an external force equal to f(t) = 16 cos(2t) + 4 sin(2t).
Find the initial conditions.
x(0)
ft
%3D
x'(0) =
ft/s
Find the particular solution.
ft
Xp =
Find the equation of motion of the mass.
x(t) =
ft
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