Question

A mass m hangs on the end of a cord around a pulley of radius a and moment of inertia I, rotating
with an angular velocity w, as shown in the figure below. The rim of the pulley is attached to a
spring (with constant k). Assume small oscillations so that the spring remains essentially
horizontal and neglect friction so that the conservation of energy of the system yields:

1/2mv^2 +1/2Iw^2+1/2kx^2-mgx=C,

where w=v/a, C=const, x+displacement from equilibrium

Find the natural circular frequency of the system in terms of m,a,k,l, and g.

ITI

Answer 1

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