A vibrational system consisting of a mass with = 0.5 kg is attached to a spring with k=1. The mass is initially released at the equilibrium position with the velocity 1 m/sec. The motion is damped with 3=1 and being driven by an external force whose period is 2 sec.

A vibrational system consisting of a mass with = 0.5 kg is attached to a spring with k=1. The mass is initially released at the equilibrium position with the velocity 1 m/sec. The motion is damped with 3=1 and being driven by an external force whose period is 2 sec.

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

4. A vibrational system consisting of a mass with m=0.5 kg is attached to a spring with k = 1.
The mass is initially released at the equilibrium position with the velocity 1 m/sec. The
motion is damped with 3-1 and being driven by an external force whose period is 2 sec.
beginning at t=0
(a) Write the IVP with the DE in normal form, and solve it for x(t).

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