Dynamics of a spring contrained string over a pulley.

[MightyG]

Homework Statement

http://img166.imageshack.us/img166/4254/tut5q3ue5.jpg

Homework Equations

The Attempt at a Solution

iv had a go at this and I think I am getting it right but just looking for a bit of clarification since my lecturer isn't giving out answers, helpfull...

ive started off by saying that initially the system is stationary and equilibrium so,

K.X_in = M.G
X_in = (M.G)/K

so MGR - K(X_in+X)R=I(alpha) sub in X_in = (M.G)/K

(MGR) - ((KMGR)/K) - (KXR) = I(alpha) simplify and sub in X=R(theta)

so,

K(R^2)(theta) + I(alpha) = 0

so (omega_N) = R SQRT(K/I)?

any help would be very very helpful!

 

[quantumdude]

Your solution is a bit hard to read. Could you possibly type it up in LaTeX? Here is a tutorial for using LaTeX at PF:

https://www.physicsforums.com/showthread.php?t=8997

Also, I don't see where you've used the $h$ anywhere. Are you using a different symbol for that?

 

[Rainbow Child]

Your calculations are correct.

@Tom Mattson for the frequency he does not need to consider $$h$$