Related Resources: vibration

Free Mass Undamped Vibration Equations and Calculator

Heat Transfer Design and Engineering

Free Mass Undamped Vibration Calculator and Equations

Spring Mass System

 

x = X cos( ω + φ)

and:

ω_n = ( k / m )^1/2

Frequency of Vibrations

f_n = ω_n / ( 2 π )

f_n = ( 1 / ( 2 π ) ) ( k / m )^1/2

f_n = ( 1 / ( 2 π ) ) ( g / x_s )^1/2

Where:

x_s = Static Deflection (m)

Periodic time:
t_p = 1 / f_n

f_n = 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.)
ω_n = (N/m/kg)^1/2
g = Gravity (9.81 m/s²)