If we attach an object weighing 8 lb to a spring, it stretched the latter by 1 ft. We attach a weight of 16 lb to this spring and it comes to rest in its equilibrium position. We assume that there is no damping and an external force F(t) = cos 3t is applied to the system. If the system is put into motion with a downward initial velocity of 2 ft per sec, a. Determine the displacement of the object. [y(t) = -; cos 4t + sin 4t + cos 3t ] b. Find the natural frequency of the mass-spring system. |Natural Frequency: o = 4]

If we attach an object weighing 8 lb to a spring, it stretched the latter by 1 ft. We attach a weight of 16 lb to this spring and it comes to rest in its equilibrium position. We assume that there is no damping and an external force F(t) = cos 3t is applied to the system. If the system is put into motion with a downward initial velocity of 2 ft per sec, a. Determine the displacement of the object. [y(t) = -; cos 4t + sin 4t + cos 3t ] b. Find the natural frequency of the mass-spring system. |Natural Frequency: o = 4]

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

If we attach an object weighing 8 lb to a spring, it stretched the latter by 1 ft. We attach a
weight of 16 lb to this spring and it comes to rest in its equilibrium position. We assume that
there is no damping and an external force F(t) = cos 3t is applied to the system. If the system
is put into motion with a downward initial velocity of 2 ft per sec,
a. Determine the displacement of the object. [y(t) = - cos 4t + sin 4t + cos 3t ]
4.
b. Find the natural frequency of the mass-spring system.
[Natural Frequency: o = 4]

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