Single Degree-of-Freedom Systems: Vibration Calculator Free SDOF System Calculator Formula Home SDOF Vibration Introduction Undamped Free Vib. Damped Free Vib. Periodic Excitation General Forcing Glossary MDOF Vibration Equations of Motion Applications SDOF Calculator Moving Vehicle Accelerometer Resources Bibliography  Login   Home Membership Magazines Forum Search Member Calculators  Materials  Design  Processes  Units  Formulas  Math 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: Kg g slug lb Stiffness, k: N/m dyne/cm Kgf/m gf/cm lbf/ft lbf/in Damping, cv: N-s/m dyne-s/cm Kgf-s/m gf-s/cm lbf-s/ft lbf-s/in Initial Displacement, x0: m cm mm ft in Initial Velocity, v0: m/s cm/s mm/s ft/s in/s
Answers
 Natural Angular Frequency, wn: 1.00  rad/s Natural Frequency, fn: 0.159  Hz Hz rpm Damping Ratio, z: 0 Damped Angular Frequency, wd: 1.00  rad/s Damped Frequency, fd: 0.159  Hz Hz rpm

Time Response

 x[t] = 1.00*Cos[1.00*t] + (0)*Sin[1.00*t] cm This system is undamped.
 For more information on unforced spring-mass systems, see SODF free vibration theory.
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