1. For the system below: a. find the differential equation in terms of 0 (for small values of 0) b. The damped natural frequency (od), and the damping ratio () (leave the answer in terms of M, C and I). c. For M=.026 lb-sec2 / in, 1 = 10 in, C = .0323 lb-sec / in, 0(0) = 10° and (0)=0, find the equation for time response 0(t) and sketch a plot of this response.

1. For the system below: a. find the differential equation in terms of 0 (for small values of 0) b. The damped natural frequency (od), and the damping ratio () (leave the answer in terms of M, C and I). c. For M=.026 lb-sec2 / in, 1 = 10 in, C = .0323 lb-sec / in, 0(0) = 10° and (0)=0, find the equation for time response 0(t) and sketch a plot of this response.

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. For the system below:
a. find the differential equation in terms of 0 (for small values of 0)
b. The damped natural frequency (od), and the damping ratio () (leave the answer in
terms of M, C and I).
c. For M=.026 lb-sec2 / in, 1 = 10 in, C = .0323 lb-sec / in, 0(0) = 10° and (0)=0, find
the equation for time response 0(t) and sketch a plot of this response.
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Step 1: Given:

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Step 2: a)To find the equation of motion:

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Step 3: b) To find the damped natural frequency and damping ratio:

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Step 4: c) To find the equation for the time response,

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Step 5: To draw the response of the system:

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