Tricky Mechanics

JohnSimpson

1. The problem statement, all variables and given/known data

See attached figure. Derive the equation of motion for the following in the parameter [tex]\theta[/tex]

2. Relevant equations



3. The attempt at a solution

The only part thats giving me trouble is the uppermost massive bar connecting the spring to the mass. I am trying to write down its kinetic energy. I know this can be decomposed as

[tex]
T = \frac{1}{2}m\bar{v}^2 + \frac{1}{2}I_{CM}\omega^2
[/tex]

where v-bar is the center of mass velocity and omega is the angular velocity of the body about its CM. I can get the first term, but I can't begin to figure out how to get Omega in the second term. I thought about considering a small change in the position of the mass, as this of course gives rise to a rotation of this bar, but the CM moves during this and it throws me off. Suggestions on how to get Omega, or on an alternative approach would be appreciated.

Attached Thumbnails

 

JohnSimpson

Hmmm, after another attempt I still can't make heads or tails of finding Omega

tiny-tim

Hi John!
?? ω = dθ/dt