7.5 Damped Harmonic Motion

• Unlike simple harmonic motion, damped harmonic motion includes an opposing damping force.
• Air resistance reduces velocity and dissipates energy of the system.
• The damping coefficient is denoted by the letter b.
• What is the key difference between the amplitudes of oscillations in simple harmonic motion and damped harmonic motion?

  Constant vs. decreasing
• In an overdamped system, there are no oscillations
• What determines the type of damping in a system?

  Strength of damping force
• What forces act on an object undergoing simple harmonic motion?

  Restoring force only
• What common forces cause damping in real systems?

  Air resistance, friction, viscosity
• How does viscosity contribute to damping?

  Internal friction
• What type of damping results in the fastest return to equilibrium without oscillations?

  Critically damped
• Underdamped systems have a weak damping force.


  True
• What does the damping coefficient (b) measure in an oscillating system?

  Strength of damping force
• If a system has a damping coefficient of 0.5 N s/m, its time constant is 2 seconds.
• In simple harmonic motion, the amplitude remains constant over time.

  True
• The primary sources of damping in real systems are air resistance, friction, and viscosity
• What does the term $e^{ - bt}$ in the equation of damped harmonic motion represent?


  Exponential decay factor
• Match the type of damping with its description:

  Underdamped ↔️ Weak damping, oscillations continue

  Overdamped ↔️ Strong damping, no oscillations

  Critically Damped ↔️ Balanced damping, fastest return to equilibrium
• What is damped harmonic motion characterized by?

  Decreasing oscillation amplitude
• In overdamped motion, the system oscillates before returning to equilibrium.

  False
• The equation for simple harmonic motion includes a damping coefficient.

  False
• Friction converts kinetic energy into heat.


  True
• Match the type of damping with its characteristic:

  Underdamped ↔️ Oscillations decrease in amplitude

  Overdamped ↔️ No oscillations, slow return to equilibrium

  Critically Damped ↔️ No oscillations, fastest return to equilibrium
• In damped harmonic motion, the amplitude decreases due to an opposing damping force.
• A critically damped system returns to equilibrium as quickly as possible without oscillations.

  True
• The amplitude of simple harmonic motion remains constant
• The oscillations in simple harmonic motion continue indefinitely.


  True
• Air resistance reduces the velocity and dissipates energy of a moving object.
• The damping coefficient in damped harmonic motion is represented by the symbol b
• An overdamped system has a strong damping force
• Which forces commonly cause damping in a pendulum's motion?

  Air resistance
• The time constant (τ) is equal to 1/b
• Match the type of damping with its characteristics:

  Underdamped ↔️ Oscillations decrease gradually

  Overdamped ↔️ No oscillations, slow return to equilibrium

  Critically Damped ↔️ Fastest return to equilibrium without oscillation
• The equation for simple harmonic motion is x(t) = A\cos(\omega t + \phi)
• The damped angular frequency $\omega'$ is related to the natural frequency $\omega$ and damping coefficient b</latex> by the equation $\omega' =$$\sqrt{\omega^{2} - b^{2}}$True
• Underdamped systems have a weak damping force, so the oscillations gradually decrease in amplitude
• In an underdamped system, oscillations gradually decrease in amplitude
• Order the types of damping from strongest damping force to weakest:

  1️⃣ Overdamped

  2️⃣ Critically Damped

  3️⃣ Underdamped
• What does the $e^{ - bt}$ term in the equation of damped harmonic motion represent?


  Exponential decay
• Match the damping type with its characteristics:

  Underdamped ↔️ Lower damping coefficient, higher time constant

  Overdamped ↔️ Higher damping coefficient, lower time constant

  Critically Damped ↔️ Balanced damping coefficient, optimal time constant
• In musical instruments, piano dampers control the length of notes