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
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 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
 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.
Glossary
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