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?

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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?
Transcribed Image Text: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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