Related Resources: vibration

Natural Frequency Undamped Two Mass Two Springs Equations and Calculator

Machine Design and Engineering

Angular Natural Frequency Undamped Two Mass Two Springs System Equations and Calculator

Mass Spring Systems in Translation Equation and Calculator

ω_n1 = [ (1/2) ( k₁ / m₁ + k₂ / m₂ ( 1 + m₂/m₁ ) + ( ( k₁/m₁ + k₂/m₂ ( 1 + m₂/m₁) )² - ( 4 k₁k₂ / ( m₁m₂)^1/2 ]^1/2
ω_n2 = [ (1/2) ( k₁ / m₁ + k₂ / m₂ ( 1 + m₂/m₁ ) - ( ( k₁/m₁ + k₂/m₂ ( 1 + m₂/m₁) )² - ( 4 k₁k₂ / ( (m₁m₂)^1/2 ]^1/2

Where:

k_1,2 = Spring Stiffness (lb/in)
m_1,2 = Mass ( lb-sec² / in )
ω_{n1, n2} = Angular Natural Frequency (rad/sec)

Reference Harris, Shock and Vibration Handbook