Quiz: Oscillations and Periodic Motion
Test your understanding of oscillations and periodic motion with these 10 questions.
1. What is simple harmonic motion?
- Any motion that is smooth and continuous
- Periodic motion where acceleration is proportional to displacement and opposite in direction
- The motion of objects falling under gravity
- Any oscillating motion regardless of the restoring force
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The correct answer is B. Simple harmonic motion (SHM) is a special type of periodic motion where the restoring force is proportional to displacement: F = -kx. This results in sinusoidal motion. Springs and pendulums (for small angles) undergo SHM, making it one of the most important oscillatory motions in physics.
Concept Tested: Simple Harmonic Motion
2. In simple harmonic motion, when is the acceleration maximum?
- When displacement is zero
- When the object passes through equilibrium
- When displacement is maximum (at the amplitude)
- Acceleration is constant in SHM
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The correct answer is C. In SHM, acceleration is proportional to displacement: a = -(ω²)x. Acceleration is maximum in magnitude when x equals the amplitude (±A). At the equilibrium position (x = 0), acceleration is zero. This is why the object moves fastest through equilibrium but has maximum acceleration at the extremes.
Concept Tested: Amplitude
3. What is the period of an oscillation?
- The maximum displacement from equilibrium
- The time required for one complete cycle of motion
- The number of oscillations per second
- The restoring force coefficient
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The correct answer is B. The period (T) is the time for one complete oscillation. It's measured in seconds. For a spring-mass system, T = 2π√(m/k). For a simple pendulum, T = 2π√(L/g). The number of oscillations per second is frequency (f), where f = 1/T.
Concept Tested: Period
4. A spring with spring constant k = 100 N/m is attached to a 0.25 kg mass. What is the period of oscillation?
- 0.314 s
- 0.628 s
- 1.0 s
- 10 s
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The correct answer is A. Period for a spring-mass system: T = 2π√(m/k) = 2π√(0.25/100) = 2π√(0.0025) = 2π(0.05) = 0.314 s. Stiffer springs (larger k) produce shorter periods, while heavier masses (larger m) produce longer periods.
Concept Tested: Hooke's Law
5. What does Hooke's Law state?
- Force equals mass times acceleration
- The restoring force of a spring is proportional to its displacement
- Energy is conserved in all systems
- Objects at rest stay at rest
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The correct answer is B. Hooke's Law states that the restoring force is proportional to displacement from equilibrium: F = -kx, where k is the spring constant. The negative sign indicates that force opposes displacement. This linear relationship holds for small displacements; large displacements may exceed the material's elastic limit.
Concept Tested: Hooke's Law
6. How does increasing amplitude affect the period of a simple pendulum?
- Period increases with amplitude
- Period decreases with amplitude
- Period remains constant (independent of amplitude for small angles)
- Period depends on whether the amplitude is increasing or decreasing
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The correct answer is C. For a simple pendulum with small angles, T = 2π√(L/g), which is independent of amplitude. This is why pendulum clocks work reliably—the period doesn't change as the pendulum loses energy and amplitude decreases. For large angles, the approximation breaks down and period depends on amplitude.
Concept Tested: Simple Pendulum
7. What is resonance?
- The amplitude of motion
- When a system is driven at its natural frequency, resulting in maximum amplitude
- The period of oscillation
- The friction in an oscillating system
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The correct answer is B. Resonance occurs when a driving force oscillates at an object's natural frequency. This causes maximum energy transfer and maximum amplitude. Dramatic examples include bridge collapses from wind or soldiers marching in step, and everyday examples include pushing a child on a swing in rhythm.
Concept Tested: Resonance
8. A mass on a spring has total mechanical energy of 10 J. At maximum displacement (amplitude), what is the kinetic energy?
- 10 J
- 5 J
- 0 J
- Depends on the mass value
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The correct answer is C. At maximum amplitude, all energy is potential energy (elastic PE for spring, gravitational PE for pendulum). All the KE has been converted to PE. As the object returns toward equilibrium, PE converts back to KE. At equilibrium, KE = 10 J and PE = 0.
Concept Tested: Simple Harmonic Motion
9. How does the period of a simple pendulum depend on its length?
- Period is independent of length
- Period is proportional to length
- Period is proportional to the square root of length
- Period is inversely proportional to length
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The correct answer is C. The period of a simple pendulum is T = 2π√(L/g). Period increases with the square root of length. Doubling the length increases the period by √2 ≈ 1.41, not by 2. This relationship is independent of mass and amplitude (for small angles).
Concept Tested: Simple Pendulum
10. Which of the following will NOT increase the amplitude of oscillation in a resonating system?
- Increasing the driving force
- Driving at the natural frequency
- Decreasing damping (friction)
- Increasing the mass of the oscillating object
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The correct answer is D. Increasing mass doesn't directly increase amplitude at resonance. While mass affects the natural frequency (heavier objects oscillate slower), at resonance the amplitude is determined by the driving force strength and damping. Increasing driving force or decreasing friction increases amplitude, as does maintaining the driving frequency equal to the natural frequency.
Concept Tested: Resonance