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

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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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

umang

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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