g_day,
OK... now you've done it! I've opened my dynamics book!
The formula for the approximate natural frequency of a cantilevered beam with a mass on the end is:
omega = 1.56 *sqrt( E * I /( m * L^3))
where,
omega is the natural frequency in radians per sec
E is Young's modulus of the beam material (207GPa for steel)
I is the second moment of inertia for the beam
m is the mass
L is the length of the beam
So you see, as the length of the beam (radius to the counterweight) increases the natural frequency of the counterweight and beam decreases very quickly.
For a given amount of energy (say your standard "1 swear-word-bump-the-forehead-on-the-back-of-the-OTA"
) as the natural frequency reduces, the amplitude of vibration increases. So any given movement or bump on the scope will cause a greater disturbance for the scope.
So I would expect that with a longer shaft and lighter counterweight, the scope will be less stable - or any movement or bumps will result in larger movement and longer time to settle.
This is why large mass and stiff stuctures are desirable things in telescopes.
Al.