Physics quiz question: spring constant of mass-spring system

Physics 5A Quiz 6, fall semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 10.32(a)

A 0.20 kg object attached to a horizontal spring oscillates left to right on a frictionless surface with a frequency of 3.5 Hz. The spring constant is:
(A) 16 N/m.
(B) 22 N/m.
(C) 97 N/m.
(D) 4.8×10² N/m.

Correct answer (highlight to unhide): (C)

The period and frequency of a mass-spring system are inverses of each other:

T = (2·π)·√(m/k),

f = 1/T = √(k/m)/(2·π).

Then the spring constant will be given by:

k = m·(2·π·f)²,

k = (0.20 kg)·(2·π·(3.5 Hz))² = 96.72212313 N/m,

which to two significant figures is 97 N/m.

(Response (A) is (1/m)(2·π/f)²; response (B) is 2·π·f, which is the angular frequency ω; while response (D) is (2·π·f)², the angular frequency squared.)

Student responses
Sections 0906, 0907
Exam code: quiz06w4v3
(A) : 3 students
(B) : 5 students
(C) : 27 students
(D) : 2 students

Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.55