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

1 question

1 item

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

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

Steps: 6

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.