5.Which expression cannot represent a solution of the wave equation?
(A)
(B)
(C)
(D)
(E) all expressions can represent a solution of the wave equation.

1. Consider a one-dimensional system with potential energy plotted below. Whichx-u diagram correctly describes a particle with energy E1 and another particle with energy E2? (A)(B)(C)(D) (E)none of the above

2. A mass m is attached to a spring with spring constant k (the other end of the spring is Exed). The mass of the spring is negligible. When the mass moves at velocity v, there is a drag force -bu acting on the mass. Which figure describes the displacement x of the mass as a function of time for some initial condition under the condition that the oscillator is overdamped?(A)(B)(C)(D)(E) none of the above

3. Consider an extra external force cosωt acting on the mass of a damped oscillator. The phenomenon "resonance" can be seen by varying ω on what kind of oscillator? (A)underdamped,(B)overdamped, (C)both kinds, (D) neitber kind, (E) resonance cannot be observed by varying w.

4. Consider a small segment of a string which is under tension T. The mass density of the string is A and the length of this segment is do. Let the vertical displacement bf the string be y(x,t) and 8y/Ox be small everywhere. The vertical force acting on this segnent is (A)(B)(C)(D)(E) none of the above.

6. The key concepts behind Kepler's 2nd law for planetary motion (the line joining the sun to a planet sweeps out equal areas in equal times) include (A)energy conser ervation,(B)momentum conservation, (C)angular momentum conservation, (D) both (a)(b), (E) both (a)(c).

7. A rocket has a mass of 2 x 108 kg. It expels gas at the rate of 2 x 10t kg/s with an exhaust speed of 1000 m/s relative to the rocket. The initial acceleration of the rocket at the launch pad (neglect gravity) is closest to (A) 1 m/s2,(B)10m/s2, (C)100 m/s2,(D) 1000m/s2,(E)100000 m/s2.

8. Water (mass density ρ) fows at speed ui； through a garden hose with cross sectional area ao and emerges at pressure ps from a nozzle of cross sectional area a0/2. The pressure at the faucet is (A)(B) (C)(D)(E) none of the above.

9. Consider N gas molecules in a cubic box of lateral size L at temperature T. Neglect the interactions between the particles and let m be the mass of a molecule, the average nunber of particles hitting one of the bounding wals per unit time is (kB is the Boltzmann constant) (A)(B) (C) (D)(E) none of the above.

10. N is the number of particles in the systen, V is the volume of the system, T is the tem- perature of the system. Which of the following is a possible expression of the entropy of a macroscopic system? (A) NIn(N/V),(B)NkBET, (C)NkBT/V, (D) NInV+N, (E) none of the above.

11. Which quantity changes during the free expansion of an ideal gas? (A)energy,(B)entropy, (C)temperature, (D) above all, .(E) none of the above.