Simple harmonic motion and energy in SHM - Question Bank

1. In SHM, the instantaneous power delivered by the restoring force is given by:
A) F * v
B) -kx * v
C) ma * v
D) All of the above
2. The equation of motion for SHM is given by d²x/dt² + ω²x = 0. What does ω represent?
A) Frequency
B) Time Period
C) Angular Frequency
D) Amplitude
3. If the amplitude of SHM is 'A', the maximum potential energy is equal to:
A) ½ mω²A²
B) mω²A
C) ½ kA
D) Zero
4. What is the energy of a particle in SHM at the extreme position?
A) Zero
B) Maximum potential energy
C) Maximum kinetic energy
D) Half of the total energy
5. What is the energy of a particle in SHM at the equilibrium position?
A) Zero
B) Maximum potential energy
C) Maximum kinetic energy
D) Half of the total energy
6. The motion of a mass on a frictionless horizontal spring is an example of:
A) Uniform circular motion.
B) Non-uniform motion.
C) Simple Harmonic Motion.
D) Random motion.
7. What is the frequency of a simple pendulum of length 1 m on Earth (g ≈ 10 m/s²)?
A) 1 Hz
B) 0.5 Hz
C) 1/(2π) Hz
D) 1/(4π) Hz
8. Which physical quantity remains constant throughout an undamped SHM?
A) Velocity
B) Acceleration
C) Kinetic Energy
D) Total Mechanical Energy
9. If the spring constant of a spring is doubled, what happens to the frequency of oscillation of a mass attached to it?
A) It doubles.
B) It is halved.
C) It increases by a factor of √2.
D) It decreases by a factor of √2.
10. In SHM, the acceleration leads the displacement by a phase angle of:
A) 0
B) π/4
C) π/2
D) π
11. In SHM, the velocity leads the displacement by a phase angle of:
A) 0
B) π/4
C) π/2
D) π
12. Which of the following represents the total energy of a particle of mass 'm' in SHM with amplitude 'A' and angular frequency 'ω'?
A) 1/2 mω²A²
B) mω²A²
C) 1/2 kA
D) mωA
13. The total energy of a particle in SHM is 10 J. What is its kinetic energy when its displacement is half the amplitude?
A) 5 J
B) 7.5 J
C) 2.5 J
D) 10 J
14. A particle is in SHM with amplitude 0.1 m and angular frequency 2 rad/s. What is its maximum velocity?
A) 0.1 m/s
B) 0.2 m/s
C) 0.05 m/s
D) 0.02 m/s
15. The angular frequency of a particle executing SHM is 5 rad/s. What is its time period?
A) 2π/5 s
B) 5/2π s
C) 10π s
D) 1/5 s
16. A system is in SHM if the net force acting on it is proportional to:
A) Velocity
B) Acceleration
C) Displacement
D) Time
17. The energy in SHM is equally divided between kinetic and potential energy at displacements:
A) x = ± A
B) x = 0
C) x = ± A/√2
D) x = ± A/2
18. If the phase difference between two SHMs of the same frequency is π/2, they are said to be:
A) In phase.
B) Out of phase.
C) In quadrature.
D) Oppositely phased.
19. What happens to the time period of SHM if the amplitude is increased, keeping other factors constant?
A) Time period increases.
B) Time period decreases.
C) Time period remains the same.
D) Time period becomes infinite.
20. What happens to the frequency of SHM if the mass is increased, keeping the spring constant the same?
A) Frequency increases.
B) Frequency decreases.
C) Frequency remains the same.
D) Frequency becomes zero.
21. The displacement-time graph for SHM is a:
A) Straight line.
B) Parabola.
C) Sine or cosine curve.
D) Hyperbola.
22. A particle executes SHM. Its potential energy is maximum at:
A) The equilibrium position.
B) The extreme positions.
C) The midpoint of its path.
D) Any point where velocity is zero.
23. A particle executes SHM. Its kinetic energy is maximum at:
A) The extreme positions.
B) The equilibrium position.
C) The midpoint of its path.
D) The start of its motion.
24. A particle executes SHM. Its velocity is zero at:
A) The equilibrium position.
B) The mean position.
C) The extreme positions.
D) The midpoint of its path.
25. Which of the following is NOT a characteristic of SHM?
A) Periodic motion.
B) Restoring force.
C) Constant velocity.
D) Oscillatory motion.
26. If a damping force is introduced in SHM, what happens to the total energy over time?
A) It increases.
B) It remains constant.
C) It decreases.
D) It oscillates.
27. The total energy in SHM is proportional to the square of which quantity?
A) Time period
B) Frequency
C) Amplitude
D) Angular frequency
28. For a simple pendulum of length 'L' undergoing small oscillations, what is its angular frequency?
A) √(g/L)
B) √(L/g)
C) √(k/m)
D) √(m/k)
29. Consider a mass 'm' attached to a spring with spring constant 'k'. What is the angular frequency of its SHM?
A) √(k/m)
B) √(m/k)
C) k/m
D) m/k
30. What is the average potential energy of a particle in SHM over one complete time period?
A) Zero
B) Half of the total energy
C) Equal to the total energy
D) Maximum potential energy
31. What is the average kinetic energy of a particle in SHM over one complete time period?
A) Zero
B) Half of the total energy
C) Equal to the total energy
D) Maximum kinetic energy
32. At what point in its oscillation is the kinetic energy equal to the potential energy in SHM?
A) At the equilibrium position.
B) At the extreme positions.
C) At x = ± A/√2.
D) At x = ± A/2.
33. If the angular frequency of an SHM is doubled, by what factor does the total energy change, keeping amplitude constant?
A) It remains the same.
B) It doubles.
C) It quadruples.
D) It increases by a factor of 8.
34. If the amplitude of an SHM is doubled, by what factor does the total energy change?
A) It remains the same.
B) It doubles.
C) It quadruples.
D) It increases by a factor of 8.
35. What is the total energy of a particle in SHM with mass 'm', angular frequency 'ω', and amplitude 'A'?
A) ½ mω²A²
B) mω²A²
C) ½ kA²
D) mωA
36. What is the kinetic energy of a particle in SHM at displacement 'x' from equilibrium, given amplitude 'A' and angular frequency 'ω'?
A) ½ mω²(A² - x²)
B) ½ mω²x²
C) ½ mω²A²
D) ½ kx²
37. What is the potential energy of a particle in SHM at displacement 'x' from equilibrium?
A) ½ kx²
B) ½ mω²x²
C) ½ mv²
D) kx
38. In SHM, when is the potential energy maximum?
A) At the equilibrium position.
B) When the velocity is maximum.
C) At the extreme positions.
D) When the kinetic energy is zero.
39. In SHM, when is the kinetic energy maximum?
A) At the extreme positions.
B) At the equilibrium position.
C) When the displacement is maximum.
D) When the acceleration is maximum.
40. What is the total mechanical energy of an ideal SHM system?
A) It varies sinusoidally with time.
B) It is zero at the equilibrium position.
C) It is constant and conserved.
D) It is maximum at the extreme positions.
41. At what position in SHM is the acceleration of the particle maximum?
A) At the equilibrium position.
B) At any position where the velocity is maximum.
C) At the extreme positions (maximum displacement).
D) At the midpoint of the oscillation.
42. At what position in SHM is the velocity of the particle maximum?
A) At the extreme positions (maximum displacement).
B) At the equilibrium position.
C) Halfway between the equilibrium and extreme positions.
D) At any position where the acceleration is zero.
43. What is the relationship between acceleration (a) and displacement (x) in SHM?
A) a = ω²x
B) a = -ωx
C) a = -ω²x
D) a = ωx²
44. Which of the following conditions is necessary for a system to exhibit SHM?
A) A constant net force acting on the system.
B) A restoring force directly proportional to the velocity.
C) A restoring force directly proportional to the displacement from equilibrium.
D) An external driving force that matches the natural frequency.
45. What is the phase constant (φ) in the equation of SHM?
A) The maximum displacement from equilibrium.
B) The total time taken for one complete oscillation.
C) The initial position of the particle at t=0.
D) The rate of change of displacement.
46. The time period (T) of a particle in SHM is related to the angular frequency (ω) by which formula?
A) T = 2πω
B) T = ω / 2π
C) T = 2π / ω
D) T = 1 / ω
47. What is the unit of angular frequency (ω) in SHM?
A) Hertz (Hz)
B) Seconds (s)
C) Radians per second (rad/s)
D) Meters per second (m/s)
48. In the equation x(t) = A sin(ωt + φ), what does 'A' represent?
A) Angular frequency
B) Phase constant
C) Amplitude
D) Time period
49. Which equation represents the displacement of a particle undergoing SHM?
A) x(t) = A sin(ωt + φ)
B) x(t) = A t² + B t + C
C) x(t) = A e^(-kt)
D) x(t) = A cos(ωt) + B sin(ωt)
50. What is the defining characteristic of Simple Harmonic Motion (SHM)?
A) The restoring force is proportional to the displacement and directed towards the equilibrium position.
B) The acceleration is constant and in the direction of motion.
C) The velocity is always zero at the equilibrium position.
D) The motion is always circular or elliptical.
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