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## Homework Statement

Show that the fractional energy lost per period is

[tex]\frac{\Delta E}{E} = \frac{2\pi b}{m\omega_0} = \frac{2\pi}{Q}[/tex]

where [tex]\omega_0 = \srqt{k/m}[/tex] and [tex]Q = m\omega_0 / b[/tex]

## Homework Equations

[tex]E = 1/2 k A^2 e^{-(b/m)t} = E_0 e^{-(b/m)t}[/tex]

## The Attempt at a Solution

[tex]\Delta E = 1/2 k A^2 e^{-(b/m)(t + T)} - 1/2 k A^2 e^{-(b/m)t}[/tex] where [tex] T = 2\pi / \omega_0[/tex]

[tex]\frac{\Delta E}{E} = e^{-(b/m)T} - 1[/tex]

[tex]\frac{\Delta E}{E} = e^{-\frac{2\pi b}{m\omega_0}} - 1[/tex]

What should I do now?

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