Physics quiz question: critical damping coefficient units

Physics 205A Quiz 1, fall semester 2017
Cuesta College, San Luis Obispo, CA

The damping ratio ζ is a dimensionless physical constant[*] used to describe the damping of masses on springs:

ζ = c_c/√(k⋅m).

The spring constant k is measured in units of kg·s^–2, and the mass m is measured in units of kg. The units for the critical damping coefficient c_c are:
(A) s.
(B) kg·s^–1.
(C) kg^–1·s.
(D) s^–1.

[*] wki.pe/Damping_ratio.

Correct answer (highlight to unhide): (B)

Starting with the expression for the critical damping coefficient c_c:

c_c = ζ·√(k⋅m),

and replacing the quantities in the equation with their kg and s units (and ζ is a dimensionless physical constant with no units), the units of c_c are:

c_c = √(kg·s^–2·kg),

c_c = √(kg²·s^–2),

c_c = kg·s^–1.

Sections 70854, 70855
Exam code: quiz01D4mP
(A) : 0 students
(B) : 42 students
(C) : 13 students
(D) : 2 students

Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.33