A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically times the instantaneous velocity. (Use g = 32 ft/s² for the acceleration due to gravity.) 8 equal to Complete the Laplace transform of the differential equation. s²£{x} + ( [ _)s£{x} + [ Use the Laplace transform to find the equation of motion x(t). x(t) = X ]) £{x} = 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically
equal to
times the instantaneous velocity. (Use g = 32 ft/s² for the acceleration due to gravity.)
8
Complete the Laplace transform of the differential equation.
s² L{x} + (₁
sL{x} +
Use the Laplace transform to find the equation of motion x(t).
x(t) =
+
+
] )L{x} = ( 0
Transcribed Image Text:A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically equal to times the instantaneous velocity. (Use g = 32 ft/s² for the acceleration due to gravity.) 8 Complete the Laplace transform of the differential equation. s² L{x} + (₁ sL{x} + Use the Laplace transform to find the equation of motion x(t). x(t) = + + ] )L{x} = ( 0
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