5.3.3 Damping and Resonance

• What is Simple Harmonic Motion (SHM)?

  Oscillatory motion with restoring force
• What is the key difference in restoring force between SHM and non-SHM?

  Direct proportionality to displacement
• What is the process of damping in SHM?

  Reducing oscillation amplitude
• What happens to oscillations in an overdamped system?

  They do not occur
• Arrange the types of damping in order from least damping to most damping.

  1️⃣ Underdamped

  2️⃣ Critically Damped

  3️⃣ Overdamped
• In an underdamped system, oscillations continue with decreasing amplitude
• Match the damping type with its damping coefficient (ζ):

  Underdamped ↔️ ζ < 1

  Critically Damped ↔️ ζ = 1

  Overdamped ↔️ ζ > 1
• What is Simple Harmonic Motion (SHM)?

  Oscillatory motion with restoring force
• Damping is the process by which the amplitude of oscillations gradually decreases over time
• What are three real-world applications where the type of damping is important?

  Car suspensions, machinery vibrations, electronic circuits
• The damping coefficient ζ characterizes the type of damping in SHM.


  True
• Resonance occurs when the driving frequency matches the natural frequency of a system.
• Increasing the mass of an oscillating system decreases its resonance frequency
• Why are car suspensions designed to be underdamped?

  To absorb bumps
• The motion pattern in SHM produces a sinusoidal displacement-time graph.


  True
• Match the examples with the type of motion:

  Pendulum at small angles ↔️ Simple Harmonic Motion

  Plucked guitar string ↔️ Non-Simple Harmonic Motion
• Critically damped systems return to equilibrium without overshooting
• Match the type of damping with its description:

  Underdamped ↔️ Oscillations decrease gradually

  Critically Damped ↔️ Returns to equilibrium quickly

  Overdamped ↔️ No oscillations occur
• The type of damping affects the stability and operation of systems like car suspensions.


  True
• Overdamped systems return to equilibrium without any oscillations
• The restoring force in SHM is always directed towards the equilibrium
• The motion in SHM is described as sinusoidal
• In underdamped systems, oscillations continue indefinitely without stopping.

  False
• Damping is important in car suspensions to reduce vibrations.


  True
• What is the key characteristic of critically damped systems?

  Fast return to equilibrium
• Critically damped systems return to equilibrium without overshooting.


  True
• In the equation of motion for damped SHM, ω_n represents the natural angular frequency
• Match the damping type with its amplitude decrease and oscillation pattern:

  Underdamped ↔️ Slow reduction, continues oscillating

  Critically Damped ↔️ Fastest reduction, no oscillation

  Overdamped ↔️ Slow reduction, no oscillation
• Match the type of damping with its description:

  Underdamped ↔️ Oscillations decrease in amplitude

  Critically Damped ↔️ No overshoot to equilibrium

  Overdamped ↔️ No oscillations occur
• Match the damping type with its damping coefficient (ζ):


  Underdamped ↔️ ζ < 1

  Critically Damped ↔️ ζ = 1

  Overdamped ↔️ ζ > 1
• At resonance, the amplitude of oscillations is significantly amplified.


  True
• What happens to the resonance frequency of a spring when its stiffness increases?

  It increases
• The collapse of the Tacoma Narrows Bridge was caused by wind-induced resonance
• The damping coefficient ζ determines the type of damping and the behavior of the system.


  True
• Order the properties of SHM in terms of their significance:

  1️⃣ Restoring Force: Always directed towards equilibrium

  2️⃣ Proportionality: Restoring force is directly proportional to displacement

  3️⃣ Motion Pattern: Produces a sinusoidal graph
• Critically damped systems have excessive damping and return to equilibrium without oscillations.

  False
• In a critically damped system, the damping is just enough to return to equilibrium as quickly as possible without overshooting
• What is the value of the damping coefficient ζ in a critically damped system?

  ζ = 1
• What is an example of resonance causing the shattering of a wine glass?

  Matching its resonant frequency
• Match the damping type with its effect on a system:

  Underdamped ↔️ Large, uncontrolled oscillations

  Critically Damped ↔️ Optimal balance, no overshoot

  Overdamped ↔️ Minimizes oscillations, sluggish response