Question

One end of a light spring with force constant 240 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 following figure, 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 2.50 cm. The pulley is free to turn on a fixed smooth axle. The vertical section of the string supports an object of mass m -250 g. The string does not slip at its contact with the pulley. The object is pulled downward a small distance and released. Ww 1n (a) What is the angular frequency of oscillation of the object in terms of the mass M? rad/s (b) What is the highest possible value of the angular frequency of oscillation of the object? rad/s (c) What is the highest possible value of the angular frequency of oscillation of the object if the pulley radius is doubled to R -5 cm? rad/s

Answer 1

Moment of inertia of pulley

I=(1/2)MR2

effective mass of the system

Angular frequency of oscillation

b)

For highest possible frequency M=0

c)

angular frequency does not depend on radius