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?
Practice Questions
1 question
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?
0.1
0.3
0.5
0.75
Damping ratio (ζ) = c / (2√(mk)) = 0.3 / (2√(1*4)) = 0.3 / 4 = 0.075.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: Damping ratio (ζ) = c / (2√(mk)) = 0.3 / (2√(1*4)) = 0.3 / 4 = 0.075.
Steps: 8
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.
