One end of a light spring with force constant k=100 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. As shown in the figure 15.61, the string changes from horizontal to vertical as it passes over a solid pulley of mass M in the shape of a solid disk of radius R=2.00 cm. The pulley is free to turn on a fixed smooth axle. The vertical section of the string supports an object of mass m=200 g. The string does not slip at its contact with the pulley. The object is pulled downward a small distance and released.
(a) What is the angular frequency ω of oscillation of the object in terms of the mass M?
(b) What is the highest possible value of the angular frequency of oscillation of the object?
(c) What is the highest possible value of the angular frequency of oscillation of the object if the pulley radius is doubled to R=4.00 cm?
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