Related Resources: vibration
Harmonic Force Constant Amplitude Applied To Base Vibration Equations
Vibration Design Formulas and Calculators
Spring Design and Engineering, Formulas
Forced damped vibration - A simple harmonic force of constant amplitude applied to base vibration Equations
Let the applied force be Fa = F cos ωt. When steady conditions are attained the mass will vibrate at the frequency of the applied force. The amplitude varies with frequency as follows:
Q = [ ( 1 + 4 R2 r2 ) / ( ( 1 - r2 )2 + 4 R2 r2 ) ]0.5
α = tan-1 ( 2 R r ) / ( 1 - r2 )
Where:
R = ωc / ωn
and
r = ω / ωn
Frequency ratio to Magnification factor ratio chart
r = Frequency ratio,
R = Damping ratio,
ωc = Critical frequency = c / ( 2 m )
ωn = spring mass system = ( k / m )0.5
1 rad/sec = 1/( 2π ) Hz
Related and Useful Links:
- Harmonic Force of Constant Amplitude Applied to Mass in Vibration Equations
- Shock and Vibration Response Equations
- Vibration Severity Chart
Reference: Mechanical Engineers Data Handbook, J. Carvill 1993