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

simple harmonic force of constant amplitude applied to base

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
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

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Reference: Mechanical Engineers Data Handbook, J. Carvill 1993