18. A particle of mass 1 kg is confined to move in the one-dimensional region x ＞ 0. It is subject to a potential energy function (Joules). If the particle is initially placed at its mechanical equilibrium position and then given a small displacement, what is the period of its subsequent oscillations?
(A)
(B)
(C)
(D)
(E) None of the above

19. Consider a uniform metal bar with both ends in contact with thermal reservoirs, one at a fixed high temperature (Th) and the other at a fixed low temperature (Tc). After reaching thermal equilibrium, which of the following statements is false? (A) The temperature gradient is a constant across the metal bar. (B) The change in entropy of the high-temperature reservoir is negative. (C) If the length of the metal bar increases, the heat flux does not change. (D) The heat flux is uniform throughout the metal bar. (E) None of the above is false.

20. Beat is an interference phenomenon when two waves of slightly different frequencies are superposed. How does the beat frequency change when both sound sources (of slightly different frequencies) move relative to the stationary listener? (A) It does not change if both sound sources approach the listener at the same speed. (B) It increases if both sound sources approach the listener at the same speed. (C) It decreases if one sound source approaches and the other moves away from the listener at the same speed. (D) It increases if one sound source approaches and the other moves away from the listener at the same speed. (E) None of the above is false.

21. John skates on the ground subject to a friction force. For a stationary observer A relative to the ground, he observes that John has an initial velocity +5 m/s in the x- direction and finally stops after traveling a distance of 12.5 m. This phenomenon is observed by the other observer B, who is riding a bus that moves at a constant speed of +2 m/s in the x-direction relative to the stationary ground. Therefore, the observer B sees that John's velocity changes from +3 m/s to -2 m/s in the x-direction. Consider the kinematic equation that, where △x is the distance travelled； which of the following statements is true? (A) From the observer B's point of view, since , B would measure a different deceleration than what A would have measured. (B) The kinematic equation only works in A's reference frame. (C) The kinematic equation only works in B's reference frame. (D) The inconsistency of the kinematic equation can be amended by the special relativity. (E) None of the above is true.

22. For a 2D monatomic ideal gas, which of the following statements is true? (A) The probability density function of finding particles of the velocity of = is not only lincarly proportional to the Boltzmann factor but also linearly proportional to y. (B) The probability density function of finding particles of the speed of v is only linearly proportional to the Boltzmann factor (C) The probability density function of finding particles of the speed v is not only linearly proportional to the Boltzmann factor but also lincarly proportional to v. (D) The probability density function of finding particles of the speed of v is not only linearly proportional to the Boltzmann factor but also linearly proportional to v2. (E) None of the above is true.

23. For two inductors connected in parallel, see the figure below； which of the following statements is true? (A) The effective inductance of the two inductors is smaller than that of both L1 and L2. (B) The effective inductance of the two inductors is larger than that of both L1and L2. (C) After a sufficiently long time, the voltage across the parallel inductors reaches a maximum steady value. (D) After a sufficiently long time, the voltage across L2 is larger than that across Li. (E) None of the above.

24. For a classical electromagnetic plane wave travelling in a vacuum, which of the following statements is true? (A) The magnetic and electric fields are perpendicular to each other, and there is a phase difference of π/2 between them. (B) The average power delivered by the EM wave increases with the frequency of the EM wave. (C) The traveling direction of the EM wave can be in either the direction of o are the direction of the electric field and the magnetic field, respectively. (D) The power of the EM wave decays as it propagates away from its source. (E) None of the above.

25. Which statement correctly describes the Bohr model of the hydrogen atom? (A) It assumes that electrons surround the hydrogen nucleus as continuous waves. (B) It succe essfully explains the fine structure of the hydrogen spectrum. (C) It assumes that the electron moves in a circular path, radiating the electromagnetic wave, (D) It assumes that the angular momentum of the electron is quantized. (E) None of the above.

26. Suppose A is a 4x4 real matrix and y,y.y,y, are four lincarly independent vectors in R4. If Av1=v1+v2, Av2=v2+v3，Av3=v3+v4, Av4=v1+v4,then how many real eigenvalues does A have? (A) 0 (B) 1 (C) 2 (D) 3 (E)4 

27. Suppose A is a 2x3 real matrix and B is a 3x2 real matrix., then which of the following matrix can be the product of BA?(A)(B)(C)(D)(E)

28. Suppose denote the standard vector norm in R2and R3. What is the smallest possible value for | As:ll if lI x=1? (A) (B) (C) 3 (D) 4(E)

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