Related Resources: vibration

Compound Pendulum Angular Natural Frequency Equations and Calculator

Machine Design and Engineering

Compound Pendulum Angular Natural Frequency Equations and Calculator

ω_n1 = [ ( a g ) / ( ρ_o² ) ] ^(1/2)

ω_n2 = [ ( a W ) / I_o ] ^(1/2)

Where:

ρ_o = Radius of Gyration abouit Axis of Support (in, m),
W = Weight of Pendulem (lb, N),
a = Distance as Indicated (ft, m),
g = Acceleration of Gravity, ( 32.2 ft/sec², 9.81 m/s² ),
I_o = Moment of Inertia About Axis of Support (in⁴, m⁴),
ω_n = Angular Natural Frequency ( rad / sec or Hz)

1 rad/sec = 1/( 2π ) Hz

Related and Useful Links:

• Section Area Moment of Inertia

Reference Harris, Shock and Vibration Handbook