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**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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