Simple harmonic motion and energy in SHM - One Line Questions

1. For a simple pendulum of length 'L' undergoing small oscillations, what is its angular frequency? — √(g/L)
2. Consider a mass 'm' attached to a spring with spring constant 'k'. What is the angular frequency of its SHM? — √(k/m)
3. In SHM, the velocity leads the displacement by a phase angle of: — π/2
4. In SHM, the acceleration leads the displacement by a phase angle of: — π
5. A particle is in SHM with amplitude 0.1 m and angular frequency 2 rad/s. What is its maximum velocity? — 0.2 m/s
6. What is the frequency of a simple pendulum of length 1 m on Earth (g ≈ 10 m/s²)? — 1/(2π) Hz
7. Which of the following represents the total energy of a particle of mass 'm' in SHM with amplitude 'A' and angular frequency 'ω'? — 1/2 mω²A²
8. What is the potential energy of a particle in SHM at displacement 'x' from equilibrium? — ½ mω²x²
9. What is the kinetic energy of a particle in SHM at displacement 'x' from equilibrium, given amplitude 'A' and angular frequency 'ω'? — ½ mω²(A² - x²)
10. What is the total energy of a particle in SHM with mass 'm', angular frequency 'ω', and amplitude 'A'? — ½ mω²A²
11. If the amplitude of SHM is 'A', the maximum potential energy is equal to: — ½ mω²A²
12. The angular frequency of a particle executing SHM is 5 rad/s. What is its time period? — 2π/5 s
13. The total energy of a particle in SHM is 10 J. What is its kinetic energy when its displacement is half the amplitude? — 7.5 J
14. What is the relationship between acceleration (a) and displacement (x) in SHM? — a = -ω²x
15. Which of the following conditions is necessary for a system to exhibit SHM? — A restoring force directly proportional to the displacement from equilibrium.
16. In the equation x(t) = A sin(ωt + φ), what does 'A' represent? — Amplitude
17. At what position in SHM is the acceleration of the particle maximum? — At the extreme positions (maximum displacement).
18. In SHM, when is the potential energy maximum? — At the extreme positions.
19. At what point in its oscillation is the kinetic energy equal to the potential energy in SHM? — At x = ± A/√2.
20. At what position in SHM is the velocity of the particle maximum? — At the equilibrium position.
21. In SHM, when is the kinetic energy maximum? — At the equilibrium position.
22. In SHM, the instantaneous power delivered by the restoring force is given by: — All of the above
23. The equation of motion for SHM is given by d²x/dt² + ω²x = 0. What does ω represent? — Angular Frequency
24. What happens to the frequency of SHM if the mass is increased, keeping the spring constant the same? — Frequency decreases.
25. What is the unit of angular frequency (ω) in SHM? — Radians per second (rad/s)
26. If the phase difference between two SHMs of the same frequency is π/2, they are said to be: — In quadrature.
27. If the spring constant of a spring is doubled, what happens to the frequency of oscillation of a mass attached to it? — It increases by a factor of √2.
28. If a damping force is introduced in SHM, what happens to the total energy over time? — It decreases.
29. If the amplitude of an SHM is doubled, by what factor does the total energy change? — It quadruples.
30. If the angular frequency of an SHM is doubled, by what factor does the total energy change, keeping amplitude constant? — It quadruples.
31. What is the total mechanical energy of an ideal SHM system? — It is constant and conserved.
32. Which of the following is NOT a characteristic of SHM? — Constant velocity.
33. The displacement-time graph for SHM is a: — Sine or cosine curve.
34. The time period (T) of a particle in SHM is related to the angular frequency (ω) by which formula? — T = 2π / ω
35. A particle executes SHM. Its velocity is zero at: — The extreme positions.
36. A particle executes SHM. Its potential energy is maximum at: — The extreme positions.
37. A particle executes SHM. Its kinetic energy is maximum at: — The equilibrium position.
38. What is the phase constant (φ) in the equation of SHM? — The initial position of the particle at t=0.
39. What is the defining characteristic of Simple Harmonic Motion (SHM)? — The restoring force is proportional to the displacement and directed towards the equilibrium position.
40. The total energy in SHM is proportional to the square of which quantity? — Amplitude
41. What happens to the time period of SHM if the amplitude is increased, keeping other factors constant? — Time period remains the same.
42. The motion of a mass on a frictionless horizontal spring is an example of: — Simple Harmonic Motion.
43. A system is in SHM if the net force acting on it is proportional to: — Displacement
44. Which physical quantity remains constant throughout an undamped SHM? — Total Mechanical Energy
45. The energy in SHM is equally divided between kinetic and potential energy at displacements: — x = ± A/√2
46. Which equation represents the displacement of a particle undergoing SHM? — x(t) = A sin(ωt + φ)
47. What is the average kinetic energy of a particle in SHM over one complete time period? — Half of the total energy
48. What is the average potential energy of a particle in SHM over one complete time period? — Half of the total energy
49. What is the energy of a particle in SHM at the equilibrium position? — Maximum kinetic energy
50. What is the energy of a particle in SHM at the extreme position? — Maximum potential energy
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