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1). A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t= 0, an external force equal to f(t) = 4 sin 4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = _? ft

1). A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t= 0, an external force equal to f(t) = 4 sin 4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = _? ft

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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1). A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t= 0, an external force equal to f(t) = 4 sin 4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g= 32 ft/s² for the acceleration due to gravity.) x(t) = _? ft 2). A mass weighing 32 pounds stretches a spring 2 feet. (a) Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s. amplititude = _? ft period = _?s (b) How many complete cycles will the mass have completed at the end of 67 seconds? cycles =
Transcribed Image Text:1). A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t= 0, an external force equal to f(t) = 4 sin 4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g= 32 ft/s² for the acceleration due to gravity.) x(t) = _? ft 2). A mass weighing 32 pounds stretches a spring 2 feet. (a) Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s. amplititude = _? ft period = _?s (b) How many complete cycles will the mass have completed at the end of 67 seconds? cycles =
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