1. Solve the following initial value problems, and determine the natural frequency, amplitude and phase angle of each solution. a. * + 100x = 0 Wn = 2+2x-0 where: x(0) = 3 and *(0) = 0 A = whorax(0) 1 and (0) 2

1. Solve the following initial value problems, and determine the natural frequency, amplitude and phase angle of each solution. a. * + 100x = 0 Wn = 2+2x-0 where: x(0) = 3 and *(0) = 0 A = whorax(0) 1 and (0) 2

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

1. Solve the following initial value problems, and determine the natural frequency, amplitude and phase
angle of each solution.
a. * + 100x = 0
Wn =
b. 2x + 3x = 0
Wn =
c. 9x + 16x = 0
Wn =
where: x(0) = 3 and x(0) = 0
A =
where: x(0) = 1 and x(0)
A =
= -2
where: x(0) = -3 and x (0) = 2
A =
8

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