What is the condition for a system to be critically damped?

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Question: What is the condition for a system to be critically damped?

Options:

Damping coefficient equals zero
Damping coefficient is less than the natural frequency
Damping coefficient equals the square root of the product of mass and spring constant
Damping coefficient is greater than the natural frequency

Correct Answer: Damping coefficient equals the square root of the product of mass and spring constant

Solution:

A system is critically damped when the damping coefficient equals the square root of the product of mass and spring constant.

What is the condition for a system to be critically damped?

Damping coefficient equals zero
Damping coefficient is less than the natural frequency
Damping coefficient equals the square root of the product of mass and spring constant
Damping coefficient is greater than the natural frequency

What is the condition for a system to be critically damped?

Correct Answer: Damping coefficient = √(mass × spring constant)

Step 1: Understand that a system can be damped in different ways: underdamped, critically damped, and overdamped.
Step 2: Know that damping refers to how oscillations in a system decrease over time.
Step 3: Identify the key components of the system: mass (m), spring constant (k), and damping coefficient (c).
Step 4: Recognize that for a system to be critically damped, it must return to equilibrium as quickly as possible without oscillating.
Step 5: Learn the mathematical condition for critical damping: c = sqrt(m * k).
Step 6: Conclude that when the damping coefficient (c) is equal to the square root of the product of mass (m) and spring constant (k), the system is critically damped.

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