- #1
rshalloo
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Homework Statement
I'm trying to derive an expression for the angular frequency of a set of springs hanging vertically down with masses in between them. 3 cases:
2 equal masses and springs.
2 different masses and equal springs
3 equal masses and springs
Homework Equations
ω0=√(k/m)
F= -kx
The Attempt at a Solution
i know its a combination of 2 fundamental modes
and that the answer I'm aiming for for the first case is (ω1^2)=((3+√5)/2)(ω0)^2 and (ω2^2)=((3-√5)/2)(ω0)^2
But i can't get there.
I did out a force diagram for the general case of 2 uneven masses and 2 springs which i hoped would do for case 1 and 2 (case1 just being a special case of case2) and came up with 2 equations of motion
ma1=-2kx1 +kx2 +(m1+m2)g
ma2=-kx2 +kx1 + m2g
I really don't know where to go from here, can someone please point me in the right direction. I am looking for someone to give me the derivation but you know that feeling when you hit a brick wall? you :P