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