4. A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 4.0 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency?
(A) 4.5 Hz
(B) 1.4 Hz
(C) 2.3 Hz
(D) 3.2 Hz
(E) 6.8 Hz

3. A 0. 125 kg harmonic oscillator has a total oscillation energy of 2.0 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency? (A) 1.4 Hz, (B) 4.5 Hz, (C) 3.1 Hz, (D) 2.3 Hz, (E) 6.4Hz.

5. An 8.0-g bullet is shot into a 4.0-kg block, at rest on a frictionless horizontal surface (see the figure). The bullet remains lodged in the block. The block moves into an ideal massless spring and compresses it by 8.7 cm. The spring constant of the spring is 2400 N/m. The initial velocity of the bullet is closest to (A) 1100 m/s. (B) 1200 m/s. (C) 900 m/s. (D) 1300 m/s. (E) 1000 m/s.

6. The mean free path of a gas molecule is:(A) the shortest dimension of the containing vessel(B) the cube root of the volume of the containing vessel(C) approximately the diameter of a molecule(D) average distance between adjacent molecules(E) average distance a molecule travels between intermolecular collisions

7. A particle with a mass of 1.0 × 10-3 g and charge of +1.0 μC is released from rest at one vertical plate of a capacitor as illustrated. If the electric field between the plates is 100 V/m, how far does the particle drop before it hits the second plate? (A) 0.49 (B) 0.98 (C) 1.96 (D) 4.9 (E) 9.8 cm

8. Consider Gauss's law: \( \oint_{S} \vec{E} \cdot d\vec{A} = q/\epsilon_0 \). (A) \( \vec{E} \) must be the electric field due to the enclosed charge (B) if \( q = 0 \) then \( \vec{E} = 0 \) everywhere on the Gaussian surface (C) if the charge inside consists of an electric dipole, then the integral is zero (D) \( \vec{E} \) is everywhere parallel to \( d\vec{A} \) along the surface (E) if a charge is placed outside the surface, then it cannot affect \( \vec{E} \) along the surface

9. Electrons (mass m, charge -e) are accelerated from rest through a potential difference V and are then deflected by a perpendicular magnetic field B. The radius of the resulting electron trajectory is: (A) \( \frac{\sqrt{2eV/m}}{B} \) (B) \( \frac{B\sqrt{2eVm}}{e} \) (C) \( \frac{\sqrt{2mV/e}}{B} \) (D) \( \frac{B\sqrt{2mV}}{e} \) (E) none of these

10. A square loop of wire moves with a constant speed v from a field – free region, through a region of uniform B field as shown. Which of the five graphs correctly shows the induced current I in the loop as a function of time t?(A) (B) (C)(D)(E)

1. 質量 2 kg 物體自長 1.6 m 斜角 30 度斜面上方自由(靜止)下滑, 測量結果顯示滑行至底部, 末速為 3.2 m/s。下列敘述何者較正確 : (A) 下滑時間為 0.5 秒 (B) 加速度為 2 m/s2 (C) 動摩擦力為 3.6 牛頓 (D) 地心引力作功, 數值為 -16 焦耳 (E) 以上皆錯誤

2. 斜拋物體以初速 \( V_0 \)，水平仰角 \( \theta \) 發射。請忽略空氣阻力。當發射體到達其軌道的頂點時，它仍擁有其起始動能的多少倍？ (A) \( \sin\theta \) (B) \( \cos(2\theta) \) (C) \( \cot\theta \) (D) \( \tan^2\theta \) (E) \( \cos^2\theta \)

3. 單一導熱介質導熱係數 k 面積為 A, 長度為 L, 兩端溫度差為 T, 熱流率為 IH。熱阻 RH=T/IH (heat resistance) 的定義與電阻 R=V/I 類似, 下列何者較正確? (A) 熱阻值 RH 與熱傳導長度 L 成正比 (B) 熱流率 IH 與介質溫差 T 成反比 (C) 熱流率 IH 與熱傳導面積 A 無關 (D) 熱傳導係數 k 類似於電阻係數 ρ (E) 以上皆錯誤

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