Machine Design

How-to, in-depth technical articles for machine design engineers

Negotiate Your Salary

Learn the best principles to negotiate the salary you deserve!

Metal 3D Printing Design Guide

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

NASA Tech Briefs

Innovations developed by NASA and its industry partners in a wide array of fields.

more free magazines
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.)

  Mass, m:    
  Stiffness, k:    
  Damping, cv:    
  Initial Displacement, x0:    
  Initial Velocity, v0:    
  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.