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What is the condition for critical damping in a damped oscillator?

Practice Questions

Q1
What is the condition for critical damping in a damped oscillator?
  1. Damping coefficient equals zero
  2. Damping coefficient equals mass times natural frequency
  3. Damping coefficient is less than mass times natural frequency
  4. Damping coefficient is greater than mass times natural frequency

Questions & Step-by-Step Solutions

What is the condition for critical damping in a damped oscillator?
  • Step 1: Understand what a damped oscillator is. It is a system that oscillates (moves back and forth) but loses energy over time due to damping (like friction).
  • Step 2: Know the terms involved: the damping coefficient (b), mass (m), and natural frequency (ω).
  • Step 3: The natural frequency (ω) is calculated using the formula ω = sqrt(k/m), where k is the spring constant.
  • Step 4: Critical damping is a special case where the system returns to equilibrium as quickly as possible without oscillating.
  • Step 5: The condition for critical damping is when the damping coefficient (b) equals 2 times the mass (m) times the natural frequency (ω).
  • Step 6: This can be written as b = 2 * m * ω.
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