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) = 2sin (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. Hint: Use g = 32 ft/s² for the acceleration due to gravity.

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) = 2sin (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. Hint: Use g = 32 ft/s² for the acceleration due to gravity.

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

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) = 2sin(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.
Hint: Use g = 32 ft/s2 for the acceleration due to gravity.

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