10. Same setup as in problem 9. Let k₁ = k₃ = k and m₁ = m₂ = m. The system oscillates with two eigenmodes. What are the corresponding eigenfrequencies? (A) (B) (C) (D) (E)

3. A solid sphere of mass m and radius r moves along a track with a circular loop of radius R1 as shown in following picture. It is released at height h. Assuming that the track has no friction, the ball thereforeslides down without rotation. Do not ignore the finite size of the sphere, what is the minimal value of h such that the sphere remains on the track at all times? (A) 2.5R − 1.5r (B) 2R − r (C) 2.5R (D) 2R + r (E) 2R − 1.5r

10. Same setup as in problem 9. Let k₁ = k₃ = k and m₁ = m₂ = m. The system oscillates with two eigenmodes. What are the corresponding eigenfrequencies?
(A)
(B)
(C)
(D)
(E)

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