Physics 3210Week 13 clicker questionsExam 3 scoresMedian 52SD 16We wish to determine the kinetic energy T=½ω•Iω, where ω is the angular velocity and I is the inertia tensor. Which frame should we use when doing the calculation?A. The body frameB. The space frameC. Some other frameWe determined the kinetic energy T=½ω•Iω in the body frame. How does this compare to the kinetic energy in the space frame?A. The kinetic energy in the space frame is less than the kinetic energy in the body frame.B. The kinetic energy in the space frame is the same as the kinetic energy in the body frame.C. The kinetic energy in the space frame is greater than the kinetic energy in the body frame.Physics 3210Wednesday clicker questionsWe found the Lagrangian of a symmetric top in a gravitational field:Which of the following quantities are conserved?I. The total energy.II. The generalized momentum associated with θ.III. The generalized momentum associated with ψ.IV. The generalized momentum associated with φ.A. I only.B. I and II.C. I, II, and III.D. I, III, and IV.E. I, II, III, and IV.   22 2 2121I cos I sin mgRcos2          LWe found that the total energy of a symmetric top in a gravitational field can be written:What motion does this equation describe?A. One-dimensional motion in θ.B. The coupling between θ and φ motion.C. The coupling between θ and ψ motion.D. The coupling between θ, φ, and ψ motion.E. None of the above. 222z112212L L cosL1E I mgRcos2I 2 2I sin    A symmetric top has total effective energy E1. What type of motion does this top undergo?A. The top is stationary.B. The top undergoes constant precession about the vertical axis.C. The top undergoes precession about the vertical axis combined with nutation.D. It cannot be determined from the information given.E1VeffθA symmetric top has total effective energy E2. What type of motion does this top undergo?A. The top is stationary.B. The top undergoes constant precession about the vertical axis.C. The top undergoes precession about the vertical axis combined with nutation.D. It cannot be determined from the information given.E2VeffθA system of two coupled harmonic oscillators has spring constants k (left spring), k12(middle spring), and k (right spring). The displacements of the blocks are measured from equilibrium. What are the forces on the blocks?A.B.kx1m mkk12x2  1 1 12 1 22 2 12 2 1F kx k x xF kx k x x        1 1 12 2 12 2 12 1 2F kx k x xF kx k x x      C.D.  1 2 12 1 22 1 12 2 1F kx k x xF kx k x x        1 12 1 2 12 12 2 1 2F k x k x xF k x k x x      For the system of two coupled harmonic oscillators, an oscillatory solution is possible ifthe amplitudes satisfyWhat type of equation is this?kx1m mkk12x21112 1222212 12BBk k kmBBk k k         A. A system of differential equations.B. A polynomial equation.C. An eigenvalue equation.D. A system of nonlinear equations.Physics 3210Friday clicker questionsFor the system of two coupled harmonic oscillators, the eigenfrequencies areWhat types of motion correspond to oscillations with the two eigenfrequencies?kx1m mkk12x21212k 2k k, mm   A. The blocks move with the same frequency. For frequency ω1: the two blocks are in phase; for frequency ω2, the two blocks are exactly out of phase.B. The blocks move with the same frequency. For frequency ω1: the two blocks are exactly out of phase; for frequency ω2, the two blocks are in phase.C. The blocks move with different frequencies.D. None of the above.A system of two coupled harmonic oscillators has spring constants k (left spring), k12(middle spring), and k (right spring). If block 1 oscillates while block 2 is held fixed, what is the frequency of oscillations? A.B.kx1m mkk12x20kmC.D.120kkm120k 2km120kkmA system of two coupled harmonic oscillators has spring constants k (left spring), k12(middle spring), and k (right spring). The displacements of the blocks are measured from equilibrium. How do the eigenfrequencies compare to the uncoupled frequencyA.B.kx1m mkk12x20 1 2  C.D.120kk?m1 0 2  1 2 0   2 0 1   A system of two coupled harmonic oscillators has spring constants k (left spring), k12(middle spring), and k (right spring). The displacements of the blocks are measured from equilibrium. If the coupling is weak (k12<<k), what is an approximate expression for the frequencyA.B.kx1m mkk12x2120kk1mk  C.D.120kk?m120kk1m 2k  120kk1mk  120kk1m 2k  A system of two coupled harmonic oscillators has weak coupling (k12<<k), and block 1 is displaced and released from rest. We found thatWhat type of motion do these equations describe?A. Harmonic oscillation of both blocks at a single frequency.B. Fast oscillation of block 1 and slow oscillation of block 2.C. Fast oscillation of block 2 and slow oscillation of block 1.D. Alternating fast and slow oscillations of the two blocks.E. Oscillation with beats: a fast oscillation modulated by a slow oscillation.kx1m mkk12x2        1 0 02 0 0x t Dcos t cos tx t Dsin t sin t   