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A mass attached to a spring oscillates with a damping coefficient of 0.3 kg/s. I

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Question: A mass attached to a spring oscillates with a damping coefficient of 0.3 kg/s. If the mass is 1 kg and the spring constant is 4 N/m, what is the damping ratio?

Options:

  1. 0.1
  2. 0.3
  3. 0.5
  4. 0.75

Correct Answer: 0.3

Solution: 

Damping ratio (ζ) = c / (2√(mk)) = 0.3 / (2√(1*4)) = 0.3 / 4 = 0.075.

A mass attached to a spring oscillates with a damping coefficient of 0.3 kg/s. I

Practice Questions

Q1
A mass attached to a spring oscillates with a damping coefficient of 0.3 kg/s. If the mass is 1 kg and the spring constant is 4 N/m, what is the damping ratio?
  1. 0.1
  2. 0.3
  3. 0.5
  4. 0.75

Questions & Step-by-Step Solutions

A mass attached to a spring oscillates with a damping coefficient of 0.3 kg/s. If the mass is 1 kg and the spring constant is 4 N/m, what is the damping ratio?
  • Step 1: Identify the given values. The damping coefficient (c) is 0.3 kg/s, the mass (m) is 1 kg, and the spring constant (k) is 4 N/m.
  • Step 2: Write down the formula for the damping ratio (ζ): ζ = c / (2√(mk)).
  • Step 3: Calculate the product of mass (m) and spring constant (k): 1 kg * 4 N/m = 4 kg·N/m.
  • Step 4: Take the square root of the result from Step 3: √(4 kg·N/m) = 2.
  • Step 5: Multiply the result from Step 4 by 2: 2 * 2 = 4.
  • Step 6: Substitute the values into the damping ratio formula: ζ = 0.3 / 4.
  • Step 7: Perform the division: 0.3 / 4 = 0.075.
  • Step 8: Conclude that the damping ratio (ζ) is 0.075.
  • Damping Ratio – The damping ratio (ζ) is a dimensionless measure that describes how oscillations in a system decay after a disturbance.
  • Spring-Mass-Damper System – A system consisting of a mass, spring, and damper that exhibits oscillatory motion influenced by damping.
  • Formula Application – Understanding and applying the formula for damping ratio, ζ = c / (2√(mk)), where c is the damping coefficient, m is the mass, and k is the spring constant.
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