Vibrations and Waves Nomenclature

Symbol	Description	Units
a	speed of wave propagation; acceleration	ft/s ; ft/s²
A	area	ft² (or in²)
A₀	amplitude of wave	ft (or in)
A, B	constants	—
c	damping coefficient	lbf·s/ft
C, D	constants	—
d	diameter	ft (or in)
f	frequency	Hz (cycles/s)
f_b	beat frequency	Hz
h	length / height	ft (or in)
I₀	modified Bessel function (1st kind, order 0)	—
J₀	Bessel function (1st kind, order 0)	—
k	spring constant	lbf/ft (or lbf/in)
K₀	modified Bessel function (2nd kind, order 0)	—
m	mass	slug or lbm
p_n	natural frequency	Hz
P	period	s
P_b	beat period	s
r	frequency ratio; radial distance	— ; ft (or in)
S	tension / force	lbf
SHM	simple harmonic motion	—
t′	thickness	ft (or in)
W	work done per cycle	ft·lbf/cycle
Y	Young’s modulus of elasticity	lbf/ft² (or psi)
ω	circular frequency	rad/s
ω_d	damped circular frequency	rad/s
ω_n	natural circular frequency	rad/s
λ	wavelength	ft
ζ	damping ratio	—
θ, φ	angles	rad
ρ	mass density	slug/ft³ (or lbm/ft³)
ρ_a	mass per area	slug/ft² (or slug/ft³)
ρ_L	mass per length	slug/ft (or lbm/ft)
μ	Poisson’s ratio	—
σ	stress	lbf/ft² (or psi)
ε	strain	—

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