T1-35
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Natural Frequency
fn = = =
where fn = natural frequency in cycles-per-second (Hz)
k = spring constant (lbs/in, N/m)
m = mass of load (lb mass, kg mass)
g = gravitational constant, 386 in/sec2 or 9.8 m/sec2
W = weight of load, m • g (lb or N)
xst = static deflectionof the spring (in or m)
fn » cycles/sec = cycles/min if xst is in inch
» cycles/sec = cycles/min if xst is in cm
Damped Natural Frequency
fdn = fn 1 – = fn
where 3 = 23 (c/ccr) = log (An/An-1) logarithmic decrement
c = damping constant (lb-sec/in or N-sec/m)
ccr = critical damping constant = 2 km
An = nth amplitude of vibration
Natural Frequency of Torsional Vibrations
ft =
where kt = torsional stiffness (lb-in/rad or N-m/rad)
I
= polar mass moment of inertia (lb-in-sec2 or kg-m2)
(continued)
Appendix 1 – Useful Formulas in Vibration Analysis
1
____
23
k
____
m
1
____
23
kg
____
W
1
____
23
g
____
xst
1
___
23
kt
___
I
(
)2
c
___
ccr
1 – 32
______
432
3.13
____
xst
188
____
xst
5
____
xst
300
____
xst
