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Spring Mass System

Spring Mass System

Frequency of Vibrations

 

x = X cos( ω + φ)

and:

ωn = ( k / m )1/2

Frequency of Vibrations

fn = ωn / ( 2 π )

fn = ( 1 / ( 2 π ) ) ( k / m )1/2

fn = ( 1 / ( 2 π ) ) ( g / xs )1/2

Where:

xs = Static Deflection (m)

Periodic time:
tp = 1 / fn

fn = Frequency of Vibrations (Hz),
x = Displacement (in, m),
X = Maximum displacement (m),
k = Spring constant / stiffness (N/m)
m = Vibrating mass (kg)
φ = Phase angle (deg.)
ωn = (N/m/kg)1/2
g = Gravity (9.81 m/s2)

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