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A damped harmonic oscillator has a mass of 2 kg and a damping coefficient of 0.5

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Question: A damped harmonic oscillator has a mass of 2 kg and a damping coefficient of 0.5 kg/s. What is the damping ratio if the spring constant is 8 N/m?

Options:

  1. 0.25
  2. 0.5
  3. 1
  4. 2

Correct Answer: 0.5

Solution: 

Damping ratio (ζ) = c / (2√(mk)) = 0.5 / (2√(2*8)) = 0.5 / (2√16) = 0.5 / 8 = 0.0625.

A damped harmonic oscillator has a mass of 2 kg and a damping coefficient of 0.5

Practice Questions

Q1
A damped harmonic oscillator has a mass of 2 kg and a damping coefficient of 0.5 kg/s. What is the damping ratio if the spring constant is 8 N/m?
  1. 0.25
  2. 0.5
  3. 1
  4. 2

Questions & Step-by-Step Solutions

A damped harmonic oscillator has a mass of 2 kg and a damping coefficient of 0.5 kg/s. What is the damping ratio if the spring constant is 8 N/m?
  • Step 1: Identify the given values: mass (m) = 2 kg, damping coefficient (c) = 0.5 kg/s, spring constant (k) = 8 N/m.
  • Step 2: Use the formula for the damping ratio (ζ): ζ = c / (2√(mk)).
  • Step 3: Calculate the product of mass (m) and spring constant (k): mk = 2 kg * 8 N/m = 16 kg·N/m.
  • Step 4: Find the square root of mk: √(mk) = √(16) = 4.
  • Step 5: Multiply the square root by 2: 2√(mk) = 2 * 4 = 8.
  • Step 6: Substitute the values into the damping ratio formula: ζ = 0.5 / 8.
  • Step 7: Calculate the damping ratio: ζ = 0.0625.
  • Damped Harmonic Oscillator – A system that experiences oscillations with a decreasing amplitude due to a damping force.
  • Damping Ratio – A dimensionless measure that describes how oscillations in a system decay after a disturbance.
  • Spring Constant – A measure of the stiffness of a spring, defined as the force required to compress or extend the spring by a unit distance.
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