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Free Vibration of SDOF Systems
The vibration frequency of unforced spring-mass-damper systems depends on their mass, stiffness, and damping values. The ensuing time-behavior of such systems also depends on their initial velocities and displacements.

To calculate the vibration frequency and time-behavior of an unforced spring-mass-damper system, enter the following values. (The default calculation is for an undamped spring-mass system, initially at rest but stretched 1 cm from its neutral position. Answers are rounded to 3 significant figures.)

Inputs
  Mass, m:    
  Stiffness, k:    
  Damping, cv:    
  Initial Displacement, x0:    
  Initial Velocity, v0:    
Answers
  Natural Angular Frequency, wn:  1.00  rad/s
  Natural Frequency, fn:  0.159  Hz
  Damping Ratio, z:  0  
  Damped Angular Frequency, wd:  1.00  rad/s
  Damped Frequency, fd:  0.159  Hz
 
Time Response

 x[t] = 1.00*Cos[1.00*t] + (0)*Sin[1.00*t] cm  Free SDOF System Calculator Related Plotter
 This system is undamped.
For more information on unforced spring-mass systems, see SODF free vibration theory.
Glossary
Negotiate Your Salary

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Essentials of Manufacturing

Information, coverage of important developments and expert commentary in manufacturing.

Metal 3D Printing Design Guide

Direct Metal Laser Sintering (DMLS) 3D printing for parts with reduced cost and little waste.

Injection Molding Design Guide

Guide for high quality and cost-effective plastic injection molding.