One end of a light spring with force constant 300 N/m is attached to a vertical

Question

One end of a light spring with force constant 300 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. The string changes from horizontal to vertical as it passes over a solid pulley of diameter 7.00 cm. The pulley is free to turn on a fixed smooth axle. The vertical section of the string supports a 600 g object. The string does not slip at its contact with the pulley. (a) Find the frequency of oscillation if the mass of the pulley is negligible. _____ Hz (b) Find the frequency of oscillation if the mass of the pulley is 150 g _____ Hz (c) Find the frequency of oscillation if the mass of the pulley is 850 g. _____ Hz

Explanation / Answer

f = w/2pi

w = sqrt(k/m+M/2)

for M=0

f = 1/2*3.14*sqrt(300/0.6+0)

f = 3.56 Hz

for M=0.15 kg

f = 1/2*3.14*sqrt(300/0.6+0.15/2) = 3.35 Hz

for M = 0.85 kg

f = 1/2*3.14*sqrt(300/0.6+0.85/2) = 2.72 Hz

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