What is the condition for critical damping in a damped harmonic oscillator?
Practice Questions
1 question
Q1
What is the condition for critical damping in a damped harmonic oscillator?
Damping coefficient equals zero
Damping coefficient equals mass times natural frequency
Damping coefficient equals twice the mass times natural frequency
Damping coefficient is less than mass times natural frequency
Critical damping occurs when the damping coefficient equals twice the mass times the natural frequency of the system.
Questions & Step-by-step Solutions
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Q
Q: What is the condition for critical damping in a damped harmonic oscillator?
Solution: Critical damping occurs when the damping coefficient equals twice the mass times the natural frequency of the system.
Steps: 5
Step 1: Understand what a damped harmonic oscillator is. It is a system that oscillates (moves back and forth) but loses energy over time due to damping (like friction).
Step 2: Identify the key terms: damping coefficient, mass, and natural frequency. The damping coefficient measures how much the motion is slowed down.
Step 3: Know the formula for critical damping. It states that critical damping occurs when the damping coefficient (c) is equal to 2 times the mass (m) times the natural frequency (ω) of the system.
Step 4: Write the condition mathematically: c = 2 * m * ω.
Step 5: Remember that critical damping is important because it allows the system to return to equilibrium as quickly as possible without oscillating.
