Related Resources: vibration

Harmonic Force of Constant Amplitude Applied to Mass in Vibration Equations

Vibration Design Formulas and Calculators
Spring Design and Engineering, Formulas

Forced damped vibration - A simple harmonic force of constant amplitude applied to mass in vibration Equations

Let the applied force be F_a = 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:

Magnitude factor Q = Actual amplitude of vibration / Amplitude for a static force F

and

Q = 1 / [ ( 1 - r² )² + 4 r² R² ]^0.5

Where:

R = ω_c / ω_n

and

r = ω / ω_n

Phase angle
α = tan^-1 ( 2 R r ) / ( 1 - r² )

Frequency ratio r = ω / ω_n

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:

• Shock and Vibration Response Equations
• Vibration Severity Chart

Reference: Mechanical Engineers Data Handbook, J. Carvill 1993