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

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

Options:

Correct Answer: Damping coefficient equals mass times natural frequency

Solution:

Critical damping occurs when the damping coefficient equals the mass times the natural frequency.

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

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.

Damped Oscillator – A system where the motion is affected by a damping force, typically proportional to the velocity.
Critical Damping – The condition where the system returns to equilibrium as quickly as possible without oscillating.
Damping Coefficient – A parameter that quantifies the amount of damping in the system.
Natural Frequency – The frequency at which a system oscillates when not subjected to any damping or external force.