Dynamic Force Calculator

Enter Engineering Inputs

Mass

Acceleration

Velocity

Displacement

Stiffness

Damping Coefficient

Excitation Frequency (Hz)

Eccentricity

Impact Duration

Dynamic Load Factor

Notes

Reset

Use consistent engineering assumptions. This tool estimates inertial, spring, damping, harmonic, unbalance, and impact-related loading in SI form.

Example Data Table

Sample values below show one realistic setup and the corresponding outputs.

Input	Sample Value	Unit
Mass	25	kg
Acceleration	12	m/s²
Velocity	1.6	m/s
Displacement	8	mm
Stiffness	45	kN/m
Damping Coefficient	320	N·s/m
Excitation Frequency	6	Hz
Eccentricity	1.5	mm
Impact Duration	30	ms
Dynamic Load Factor	1.25	—

Output	Example Result
Inertial Force	300.00 N
Spring Force	360.00 N
Damping Force	512.00 N
Unbalance Force	53.30 N
Harmonic Force	284.24 N
Impact Average Force	1333.33 N
Natural Frequency	6.75 Hz
Damping Ratio	0.151
Dynamic Amplification Factor	2.94
Conservative Design Force	4496.31 N

Formula Used

Inertial force: F_i = m × a

Spring force: F_s = k × x

Damping force: F_d = c × v

Harmonic force: F_h = m × ω² × x

Unbalance force: F_u = m × e × ω²

Impact average force: F_impact = m × Δv / Δt

Natural frequency: f_n = (1 / 2π) × √(k / m)

Damping ratio: ζ = c / (2 × √(k × m))

Frequency ratio: r = f / f_n

Dynamic amplification factor: DAF = 1 / √((1 − r²)² + (2ζr)²)

Conservative design force: F_design = (|F_i| + |F_s| + |F_d| + |F_u|) × DLF × DAF

The conservative design force uses absolute component magnitudes before applying the dynamic load factor and amplification factor.

How to Use This Calculator

Enter mass, acceleration, and velocity for the moving system.
Add displacement, stiffness, and damping to describe structural response.
Enter excitation frequency to evaluate vibration-related amplification.
Use eccentricity when rotating unbalance exists in the machine or component.
Enter impact duration if shock or sudden stopping occurs.
Set a dynamic load factor to reflect design conservatism or project standards.
Press the calculate button to show results above the form.
Use the export buttons to save the result set as CSV or PDF.

FAQs

1) What is dynamic force?

Dynamic force is a time-varying load created by motion, vibration, impact, or changing acceleration. It often differs from a simple constant static load.

2) How is dynamic force different from static force?

Static force remains steady. Dynamic force changes with time, velocity, acceleration, frequency, or shock, so it can create much higher peak loads.

3) Why is the dynamic load factor included?

The dynamic load factor adds design margin for uncertain loading, shock severity, installation conditions, or code-based conservatism in engineering calculations.

4) Why does damping ratio matter?

Damping ratio controls how strongly vibration grows near resonance. More damping usually reduces amplification and lowers the expected peak response.

5) What does the frequency ratio show?

It compares excitation frequency to natural frequency. A ratio near one suggests resonance risk and a potentially large amplified response.

6) Can I use impact duration for shock loading?

Yes. Shorter impact time produces a larger average force for the same mass and speed change, making it useful for shock screening.

7) Why is the governing peak force sometimes much larger?

Peak force may exceed the signed sum because the tool checks conservative component magnitudes, amplification, and impact force separately before selecting the governing value.

8) Which units are supported?

The calculator supports common SI and selected imperial units for mass, acceleration, velocity, displacement, stiffness, damping, and impact duration.