A solid cylider of mass 9.8 kg and radius 28 cm is yoked to a spring as shown. T

Question

A solid cylider of mass 9.8 kg and radius 28 cm is yoked to a spring as shown. To be precise, the axle of the cylinder is attached to a horizontal spring force constant 2679 N/m. The cylinder rolls back and forth on a horizontal base without slipping. From simplicity, assume that the spring, he axle and the yoke which connects them have negligible masses compared to the cylinder itself. What is the angular frquency of the cylinder rolling back and foth around the equilibrium position?

Answer in units of s^-1

Explanation / Answer

using conservation of energy

1/2kx^2+1/2Iw^2+1/2mv^2=0

1/2kx^2+1/2*mr^2/2*v^2/r^2+1/2*mv^2=0

1/2kx^2+3/4mv^2=0

differentiating wrt time

kx+3/2ma=0

angular frquency=sq rt of(3k/2m)=20.23

f=20.23/(2*3.14)=3.222 s^-1

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