Jen is working on a springmassdamper system She remembers fr

Jen is working on a spring-mass-damper system. She remembers from her dynamic systems class that the damping ratio zeta is a nondimensional property of such systems and that zeta is a function of spring constant k, mass m, and damping coefficient c. Unfortunately, she does not recall the exact form of the equation for However, she is taking a fluid mechanics class and decides to use her newly acquired knowledge abeut dimensional analysis to recall the form of the equation. Help Jen develop the equation for zeta using the methed of repeating variables. Identify the exact functional relationship.

Solution

>> Let, \"z\" is the Damping Ratio

and, as ,

z = c/(2mw)

where, w = natural Frequency = (k/m)^1/2

=> Damping Ratio, z = c/[2m*(k/m)^1/2 ] = c/[2(mk)^1/2

So, Option (C) ....is Correct...........ANSWER.......