Exploring Harmonic Motion

What are the key characteristics of simple harmonic motion?

• Key characteristics of simple harmonic motion include periodicity, sinusoidal nature, constant frequency, restoring force proportional to displacement, and maximum amplitude.

• Constant acceleration

• Non-periodic motion

• Restoring force inversely proportional to displacement

How does the displacement of an object in simple harmonic motion relate to time?

• The displacement follows a linear function.

• The displacement is constant over time.

• Displacement is only affected by mass and not time.

• The displacement of an object in simple harmonic motion relates to time through a sinusoidal function.

Sketch a graph representing the displacement of a simple harmonic oscillator over time.

• The graph shows random fluctuations with no clear pattern.

• The graph is a straight line indicating constant displacement.

• The graph is a triangle wave, alternating between sharp peaks and troughs.

• The graph is a sinusoidal wave, oscillating between maximum and minimum displacements.

What is the formula for the period of a simple harmonic oscillator?

• T = 2π√(m/k)

• T = 2π√(k/m)

• T = √(m/k)

• T = 2π(m/k)

Describe one real-world application of simple harmonic motion.

• Rubber bands exhibit simple harmonic motion when stretched.

• Cars use simple harmonic motion for suspension systems.

• Pendulum clocks utilize simple harmonic motion for accurate timekeeping.

• Waves in the ocean are examples of simple harmonic motion.

What is the effect of damping on the amplitude of oscillations?

• Damping increases the amplitude of oscillations.

• Damping decreases the amplitude of oscillations.

• Damping has no effect on the amplitude of oscillations.

• Damping only affects the frequency of oscillations.

Explain the difference between underdamped, critically damped, and overdamped systems.

• Underdamped: oscillates, Critically damped: fastest return without oscillation, Overdamped: slow return without oscillation.

• Underdamped: no oscillation, Critically damped: slow return with oscillation, Overdamped: oscillates rapidly.

• Underdamped: fastest return with oscillation, Critically damped: oscillates slowly, Overdamped: immediate stop without oscillation.

• Underdamped: slow return with oscillation, Critically damped: oscillates, Overdamped: fastest return without oscillation.

How does the damping coefficient affect the motion of a damped harmonic oscillator?

• The damping coefficient has no effect on the motion of the oscillator.

• The damping coefficient increases the frequency of oscillation.

• The damping coefficient affects the rate of amplitude decay and the type of motion (underdamped, critically damped, overdamped) in a damped harmonic oscillator.

• The damping coefficient only affects the initial position of the oscillator.

What is resonance in the context of harmonic systems?

• Resonance is the process of damping vibrations in a system.

• Resonance occurs when a system is forced to oscillate at a frequency lower than its natural frequency.

• Resonance is the phenomenon where a system remains static without any oscillation.

• Resonance is the phenomenon where a harmonic system oscillates with increased amplitude at its natural frequency.

Provide an example of resonance in everyday life.

• A singer shattering a wine glass by matching its natural frequency.

• A dog barking at a passing car.

• A child playing with a swing at the park.

• A car engine running smoothly due to proper tuning.