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Old Dec 12th 2011, 10:52 AM   #1
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Damped Oscillator equation. Finding Energy and general solution for coupled oscillato

Hi! I can do (a) easily enough but (b) has me totally stumped altogether! I can't seem to figure out how they get it in that form! Also (c) I'm having the same problem. I have two exams tomorrow and this is the first one so im juggling between the two subjects going through the past papers so if anyone could help with a solution for this it would be very helpful! Thanks


1. (a) The damped oscillator equation

m d2y/dt2 + dy/dt + ky = 0 has a solution of the form
y(t) = Ae−α t cos(wt − ϕ ).
Determine α and ϕ.

(b) Show that the energy of the system in (a) given by E = 1/2mẋ^2 + 1/2kx^2
satisfies dE/dt = −mvẋ

(c) Two coupled oscillators are described by the equations
mẍ1 = −kx1 + k(x2 − x1)
mẍ2 = −k(x2 − x1) − kx2.
Construct the general solution (normal modes) for this system.
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Old Dec 12th 2011, 03:09 PM   #2
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I'm going to bed now, couldn't find the answer to this? Its late here in Ireland and i'm up early tomorrow for my exam so hopefully when I wake up someone might of been able to answer it from a different time zone?! Thanks
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coupled, damped, energy, equation, finding, general, oscillato, oscillator, solution



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