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

₹0.0

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

Options:

Correct Answer: Damping coefficient equals twice the mass times natural frequency

Solution:

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

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

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

Correct Answer: Damping coefficient = 2 * Mass * Natural frequency

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.

Damped Harmonic Oscillator – A system where the motion is affected by a damping force, leading to a decrease in amplitude over time.
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 external force.