Coupled Vertical Oscillators with Gravity

[mekrob]

Hey, I'm just having some trouble getting started with this problem.

-------------
(
)
(
m1
(
)
(
2m1
Crude representation: (The parantheses are supposed to be the springs)

There is a mass (m1) that is attached vertically to a board by a spring of spring constant k and length b. There is a second mass (2m1) attached by an identical spring to the first mass.

I'm supposed to find the normal frequencies in a constant (so it isn't affected by x1 and x2, right?) gravitational field and the normal coordinates. I can do coupled oscillators pretty easily, but I'm just having a hard time setting it up.

Best guess...
m1x1'' = -k1x1 +k2(x2-x1) + g
m2x2'' = k2x2 + g

I guess I'm not exactly sure where g goes into the MX''=-Kx matrix.

 

[nrqed]

Hey, I'm just having some trouble getting started with this problem.

-------------
(
)
(
m1
(
)
(
2m1
Crude representation: (The parantheses are supposed to be the springs)

There is a mass (m1) that is attached vertically to a board by a spring of spring constant k and length b. There is a second mass (2m1) attached by an identical spring to the first mass.

I'm supposed to find the normal frequencies in a constant (so it isn't affected by x1 and x2, right?) gravitational field and the normal coordinates. I can do coupled oscillators pretty easily, but I'm just having a hard time setting it up.

Best guess...
m1x1'' = -k1x1 +k2(x2-x1) + g
m2x2'' = k2x2 + g

I guess I'm not exactly sure where g goes into the MX''=-Kx matrix.

Just shift x_2. It's easy to get a shifted x_2 that will get rid of the g in both equations. Than you can solve the usual way and in the final solution you can go back to the original x_2