A convenient way to measure damping in a single-degree-of-freedom system is called logarith- mic decrement of free response. Consider the free response given by (4). Let's denote t₁ and t₂ denote the times corresponding to two consecutive displacements ₁ and 2 measured one cycle apart, i.e., where t₂ = t₁ + T T = 2π Wd According to (4), show that the logarithmic decrement dis x1 8 = log = (WnT X2 where log has base e. Combine (5), (7), and (8) to obtain 8 √47² +8² Will this method work for other initial conditions? why?

A convenient way to measure damping in a single-degree-of-freedom system is called logarith- mic decrement of free response. Consider the free response given by (4). Let's denote t₁ and t₂ denote the times corresponding to two consecutive displacements ₁ and 2 measured one cycle apart, i.e., where t₂ = t₁ + T T = 2π Wd According to (4), show that the logarithmic decrement dis x1 8 = log = (WnT X2 where log has base e. Combine (5), (7), and (8) to obtain 8 √47² +8² Will this method work for other initial conditions? why?

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 convenient way to measure damping in a single-degree-of-freedom system is called logarith-
mic decrement of free response. Consider the free response given by (4). Let's denote t₁ and
t2 denote the times corresponding to two consecutive displacements ₁ and 2 measured one
cycle apart, i.e.,
where
t₂ = t₁ + T
2π
Wd
According to (4), show that the logarithmic decrement dis
T =
x1
8 = log =
x2
where log has base e. Combine (5), (7), and (8) to obtain
= (WnT
8
4π² +8²
Will this method work for other initial conditions? why?

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