(adsbygoogle = window.adsbygoogle || []).push({}); Consider damped harmonic oscillations. Let the coeffient of friction gamma be half the value of the one that just gies critical damping.

How many times is the period T larger than it would be for gamma = 0??

WHen gamma is zero -

[tex] T = \frac{2 \pi}{\omega} [/tex]

When gamma is half of the value for critical damping

now for critical damping

[tex] \frac{\gamma}{2} = \omega_0 [/tex]

So then for the question, (half of the value for gamma) then

that yields omega / 2

and then gives a period [tex] T = \frac{2 \pi}{\frac{\omega}{2}} [/tex]

and that gives [tex] T = \frac{4 \pi}{\omega} [/tex]

which is half the period for the case when gamma is zero

My text book says the answer - the ratio between T(damped) and T(undamped) = 2 / root(3)

Determine the ratio between two successive swings on teh same side.

It doesn't quite give the case for WHICH case it wants us to consider but it is definitely related to the previous question

I am completely baffled as to how to go about this

do i plug this into the equation for the damping that is

[tex] = x = x_0 e^{\frac{\gamma t}{2}} Cos(\omega_d t + \theta) [/tex]

Answer of the text is X2/X1 = exp (-2pi / 3) i dont know how

i am not sure

your help is greatly appreciated!!

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# Homework Help: Some help with oscillations and damping

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