**Related Resources: vibration**

### Simple harmonic force rotary unbalance

Vibration Design Formulas and Calculators

** Spring Design and Engineering, Formulas**

**Forced damped vibration - A simple harmonic force applied to mass due to rotary unbalance vibration Equations **

F = m_{r}·a·ω^{2}·cos ( ω · t )

(due to mass m_{r}, rotating at radius a
angular velocity ω)

The amplitude varies with frequency as follows:

Q = - r^{2} / [ ( 1 - r^{2} )^{2} + 4 R^{2} r^{2} ) ]^{0.5}

α = tan^{-1} ( 2 R r ) / ( 1 - r^{2} )

Where:

R = ω_{c} / ω_{n}

and

r = ω / ω_{n}

Frequency ratio to Magnification factor ratio chart

r = Frequency ratio,

R = Damping ratio,

ω_{c} = Critical frequency = c / ( 2 m )

ω_{n} = spring mass system = ( k / m )^{0.5}

1 rad/sec = 1/( 2π ) Hz

Related and Useful Links:

- Harmonic Force Constant Amplitude Applied To Base Vibration Equations
- 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