Introductory Electricity And Magnetism — 2025 Past Questions

University of Ilorin PHY104: 23 questions.

Topics: Simple harmonic motion, Waves

1. At resonance, amplitude is
   1. Constant
   2. Zero
   3. Maximum
   4. Minimum
2. Two waves are given by Acos(150πt - 24x) and Acos(250πt - 4x). What is the beat frequency?
   1. 50 Hz
   2. 25 Hz
   3. 100 Hz
   4. 200 Hz
3. What is the relationship between wave velocity and tension in a string?
   1. v ∝ √T
   2. v ∝ T
   3. v ∝ T²
   4. v ∝ 1/T
4. Which of the following terms represents the envelope in damped oscillations?
   1. sin(kx - ωt)
   2. cos(kx - ωt)
   3. exp(-γt/2)
   4. tan(kx - ωt)
5. The normal mode of a system is also known as
   1. Free oscillation
   2. Resonance state
   3. Natural frequency
   4. Periodic motion
6. The degree of freedom of a system with a mass with springs connected on either end is
   1. 0
   2. 1
   3. 2
   4. 3
7. In damped oscillations, if initial energy E₀ = 20 J and relaxation time τ = T, what is the energy after t = 2T?
   1. 0 J
   2. 10 J
   3. 15 J
   4. 20 J
8. What is the formula for relaxation time in damped oscillations?
   1. τ = b/2m
   2. τ = 2m/b
   3. τ = 2m
   4. τ = 2mb
9. What is the relationship between tension and frequency in a string?
   1. T/f = constant
   2. T/f² = constant
   3. f ∝ T
   4. f ∝ T²
10. Which of the following occurs in coupled oscillations?
    1. Damping
    2. Energy is transferred
    3. Frequency increases
    4. Amplitude remains same
11. In a dispersive medium, wave components have
    1. Same velocity and same frequency
    2. Different velocity and same frequency
    3. Different velocity and different frequency
    4. Same velocity and different frequency
12. For a mass moving in the same direction with same displacement with spring constants kₐ and k_b on either side, the equation of motion is
    1. ma = (kₐ + k_b)x
    2. ma = -(kₐ + k_b)x
    3. ma = (kₐ - k_b)x
    4. ma = -(kₐ - k_b)x
13. If the Q factor is 20, how many oscillations occur when the energy is halved?
    1. 20/π
    2. 40/π
    3. 10/π
    4. 5/π
14. When a mass is attached to a spring, how many degrees of freedom does it have?
    1. Zero
    2. One
    3. Two
    4. Three
15. When two masses are connected by three springs, how many degrees of freedom will it have?
    1. One
    2. Two
    3. Three
    4. Four
16. What can be derived from the wave equation?
    1. Speed
    2. Velocity
    3. Wavelength
    4. Frequency
17. Two springs with constants k₁ = 16 N/m and k₂ = 20 N/m are connected to a mass m = 5 kg. Calculate the angular frequency
    1. √(36/5)
    2. √(20/5)
    3. √(16/5)
    4. √(18/5)
18. For y(x,t) = 0.25cos(240t - 0.5x), calculate the wave velocity
    1. 120 m/s
    2. 480 m/s
    3. 240 m/s
    4. 0.5 m/s
19. A body in oscillation has a mass of 250 g and a force constant of 16 N/m. Find the frequency and period of the oscillation
    1. f = 2 Hz, T = 0.5 s
    2. f = 4 Hz, T = 0.25 s
    3. f = 1 Hz, T = 1 s
    4. f = 8 Hz, T = 0.125 s
20. Which of the following is correct for a classical wave equation?
    1. ∂²ψ/∂t² = v² ∂²ψ/∂x²
    2. ∂ψ/∂t = v ∂ψ/∂x
    3. ∂²ψ/∂t² = -v² ∂²ψ/∂x²
    4. ∂ψ/∂t = -v ∂ψ/∂x
21. A mass-spring system has a mass of 250 g and spring constant 10 N/m. Calculate the frequency and period
    1. 1.62 Hz, 0.62 s
    2. 1.62 Hz, 0.79 s
    3. 1.27 Hz, 0.79 s
    4. 1.56 Hz, 0.66 s
22. What causes the amplitude of an oscillating system to decrease over time?
    1. Decrease in frequency
    2. Increase in restoring force
    3. Change in spring constant
    4. Energy loss due to damping
23. A system has a Q factor of 20. How many oscillations occur before the energy is halved?
    1. 10/π
    2. 5/π
    3. 10/π
    4. 20/π

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