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After a mass weighing 10 lbs. is attached to a 5 ft. spring, the spring measures 7 ft. This mass is removed and replaced with another mass that weighs 8 lbs. The entire system is placed in a medium that offers a damping force that is numericallly equal to the instantaneous velocity. The mass is then initially released from a point ½ ft below the equilibrium position with a downward velocity of 1 ft/s Given that the equation of motion is x(t) =te"(cos 4t + sin 41) a) Express the equation of motion in the form x(t) = Ae sin(V@? – 2²t+ø) where A=Vcỉ +c; and %3D tan o =

After a mass weighing 10 lbs. is attached to a 5 ft. spring, the spring measures 7 ft. This mass is removed and replaced with another mass that weighs 8 lbs. The entire system is placed in a medium that offers a damping force that is numericallly equal to the instantaneous velocity. The mass is then initially released from a point ½ ft below the equilibrium position with a downward velocity of 1 ft/s Given that the equation of motion is x(t) =te"(cos 4t + sin 41) a) Express the equation of motion in the form x(t) = Ae sin(V@? – 2²t+ø) where A=Vcỉ +c; and %3D tan o =

Advanced Engineering Mathematics
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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6. After a mass weighing 10 lbs. is attached to a 5 ft. spring, the spring measures 7 ft. This mass is removed and replaced with another mass that weighs 8 lbs. The entire system is placed in a medium that offers a damping force that is numerically equal to the instantaneous velocity. The mass is then initially released from a point ½ ft below the equilibrium position with a downward velocity of 1 ft/s Given that the equation of motion is x(t) = e (cos 4t + sin 4t) a) Express the equation of motion in the form x(t) = Ae¯ sin(vo? – 2°t+p) where A=Veỉ +c and - At tan o : C2 b) Find the time at which the mass passes through the equilibrium position heading upward.
Transcribed Image Text:6. After a mass weighing 10 lbs. is attached to a 5 ft. spring, the spring measures 7 ft. This mass is removed and replaced with another mass that weighs 8 lbs. The entire system is placed in a medium that offers a damping force that is numerically equal to the instantaneous velocity. The mass is then initially released from a point ½ ft below the equilibrium position with a downward velocity of 1 ft/s Given that the equation of motion is x(t) = e (cos 4t + sin 4t) a) Express the equation of motion in the form x(t) = Ae¯ sin(vo? – 2°t+p) where A=Veỉ +c and - At tan o : C2 b) Find the time at which the mass passes through the equilibrium position heading upward.
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