Converting from lb_f/in to N/m issues

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The discussion centers on converting units from lb_f/in to N/m for calculating the damping ratio in a physics problem. The user has converted the spring constant, mass, and damping coefficient but questions the validity of their results, particularly the unusually high damping ratio of 1000.26. They express confusion over the definition of natural frequency (ω_n) and acknowledge a mistake in their calculations regarding the mass and spring constant relationship. The conversation highlights the importance of accurate unit conversions and understanding the underlying equations in dynamics. Clarifying these aspects is essential for obtaining correct results in mechanical systems.
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Homework Statement


I am trying to find a damping ratio. I know ##k=50## lb##_f##/in, ##m=50## lb, ##c = 0.75## lb##_f##-sec/in.

Homework Equations


##1## lb##_f##/in = ##175.1268## N/m
##1## lb = ##0.4536## kg

The Attempt at a Solution


Then ##k = 8756.34## N/m, ##c = 131.345## N/m-sec, and ##m = 22.675## kg.
$$
\zeta = \frac{c}{2\omega_nm} = \frac{131.345}{2(0.00259)(22.675)} = 1000.26
$$
but this seems awfully large. Are my conversion factors incorrect?
 
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How is ##\omega_n## defined?
 
vela said:
How is ##\omega_n## defined?

Thanks. I divided m by k instead of the other way around.
 

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