# 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.

### 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.

### How to Use the Calculator

#### 1. Basic Calculator

**Enter Spring Constant (N-m)**: Input the spring constant value to find the damping ratio or mass.**Example**: 25 N-m

**Enter Mass (kg)**: Input the mass value to find the damping ratio or spring constant.**Example**: 10 kg

**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

**Enter Spring Constant (N-m)**: Provide the spring constant value.**Example**: 50 N-m

**Enter Mass (kg)**: Provide the mass value.**Example**: 20 kg

**Enter Damping Coefficient (Ns/m)**: Provide the damping coefficient.**Example**: 5 Ns/m

### Formula

$\text{DMP}=2\times \sqrt{k\times m}$

**$ Variables$**

Variable | Description |
---|---|

$\text{DMP}$ | 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:

$\text{DMP}=2\times \sqrt{k\times m}$

3. Calculation:

$\text{DMP}=2\times \sqrt{25\times 10}$

4. Simplify:

$\text{DMP}=2\times \sqrt{250}$

5. Result:

$\text{DMP}=2\times 15.81=31.62$

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:

$\text{DMP}=2\times \sqrt{k\times m}$

3. Calculation:

$\text{DMP}=2\times \sqrt{50\times 20}$

4. Simplify: $\text{DMP}=2\times \sqrt{1000}$

5. Result: $\text{DMP}=2\times 31.62=63.24$

Thus, the damping ratio is 63.24.

Thank you for using our tool.