A solid disk of mass M and radius R is on a vertical shaft. The shaft is attached to a coil spring that exerts a linear restoring torque of magnitude Cθ, where θ is the angle measured from the static equilibrium position and C is a constant. Neglect the mass of the shaft and the spring, and assume the bearings to be frictionless.
(a) Show that the disk can undergo simple harmonic motion, and find the frequency of the motion.
(b) Suppose that the disk is moving according to θ = θ0 sin (ωt), where ω is the frequency found in part (a). At time t1 = π/ω, a ring of sticky putty of mass M and radius R is dropped concentrically on the disk. Find:
(1) The new frequency of the motion.
Ei = Ef
The Attempt at a Solution
to get w=w0/√3
I don't understand why if energy is conserved (I know E is always conserved) helps? why just rotational, the putty is moving down with speed and height?! Too many unknowns!
conservation of angular momentum equation has 2 unknowns..
Thanks for any help[/B]