Damping Ratio Calculator

How to quickly find the damping ratio of a system? Enter specific values into the Damping ratio calculator, you can easily determine the damping ratio, mass, or spring constant.

Damping Ratio Calculator

The spring constant (N-m) is a measure of a spring’s stiffness.

The mass (kg) of the object attached to the spring.

The damping ratio is a dimensionless measure describing how oscillations decay.

What is Damping Ratio?

The damp ratio checks how wobbles in a thing fade after a bump. It shows how the thing fights wiggle. A high damp ratio means the thing settles fast. A low ratio means wobbles last longer. The ratio tells us how bouncy or calm the thing acts after trouble starts. It helps know if it wiggles for a long time or chills out quick once the bump is gone.

Damping Ratio Calculator Formula

How to Use the Calculator

1. Basic Calculator

  1. Enter Spring Constant (N-m): Input the spring constant value to find the damping ratio or mass.
    • Example: 25 N-m
  2. Enter Mass (kg): Input the mass value to find the damping ratio or spring constant.
    • Example: 10 kg
  3. Enter Damping Ratio: Input the damping ratio to find the spring constant or mass.
    • Example: Leave this field empty to calculate it.

2. Advanced Calculator

  1. Enter Spring Constant (N-m): Provide the spring constant value.
    • Example: 50 N-m
  2. Enter Mass (kg): Provide the mass value.
    • Example: 20 kg
  3. Enter Damping Coefficient (Ns/m): Provide the damping coefficient.
    • Example: 5 Ns/m

Damping Ratio Formula

DMP=2×k×m

Variable Description
DMP Damping Ratio
k Spring Constant (N-m)
m Mass (kg)

How to Calculate Damping Ratio

Example 1

Given Values

  • Spring Constant: 25 N-m
  • Mass: 10 kg
  • Damping Ratio: (to be calculated)

Calculation:

1. Given:

  • k=25
  • m=10

2. Formula:

DMP=2×k×m

3. Calculation:

DMP=2×25×10 

4. Simplify:

DMP=2×250

5. Result:

DMP=2×15.81=31.62

Thus, the damping ratio is 31.62.

 

Example 2

Given Values are:

  • Spring Constant: 50 N-m
  • Mass: 20 kg
  • Damping Ratio: (to be calculated)

Calculation:

1. Given:

  • k=50
  • m=20

2. Formula:

DMP=2×k×m

3. Calculation:

DMP=2×50×20

4. Simplify:

DMP=2×1000

5. Result:

DMP=2×31.62=63.24

Thus, the damping ratio is 63.24.

 

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