Q4 A mass M is attached to a massless hoop of radius R that lies in a vertical plane. The hoop is free to rotate about its fixed center. M is tied to a string which winds part way around the hoop, then rises vertically up and over a massless pulley. A mass m hangs on the other end of the string. M (a) Find the equation of motion for the angle of rotation of the hoop. (b) What is the frequency of small oscillations? Assume that m moves only vertically, and assume M > m. m
Q4 A mass M is attached to a massless hoop of radius R that lies in a vertical plane. The hoop is free to rotate about its fixed center. M is tied to a string which winds part way around the hoop, then rises vertically up and over a massless pulley. A mass m hangs on the other end of the string. M (a) Find the equation of motion for the angle of rotation of the hoop. (b) What is the frequency of small oscillations? Assume that m moves only vertically, and assume M > m. m
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Transcribed Image Text:Q4
A mass M is attached to a massless hoop of radius R that lies in a
vertical plane. The hoop is free to rotate about its fixed center. M
is tied to a string which winds part way around the hoop, then
rises vertically up and over a massless pulley. A mass m hangs on
the other end of the string.
M
(a) Find the equation of motion for the angle of rotation of the hoop.
(b) What is the frequency of small oscillations?
Assume that m moves only vertically, and assume M > m.
m
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