Physics quiz question: comparison of mass-spring periods

Physics 205A Quiz 6, fall semester 2017
Cuesta College, San Luis Obispo, CA

A mass of 0.100 kg hangs from a k = 10.0 N/m spring, while a mass of 2.20 kg hangs from a k = 200.0 N/m spring[*][**]. The __________ system will have a longer oscillation period.
(A) 0.100 kg mass, 10.0 N/m spring.
(B) 2.20 kg mass, 200.0 N/m spring.
(C) (There is a tie.)
(D) (Not enough information is given.)

[*] eiscolabs.com/products/ph0323ss?variant=6635998660.
[**] google.com/shopping/product/3295840510445490103.

Correct answer (highlight to unhide): (B)

The period T of a mass m attached to a spring with spring constant k is given by:

T = 2·π·√(m/k).

For the 0.100 kg mass, 10.0 N/m spring system, the period is:

T = 2·π·√((0.100 kg)/(10.0 N/m)) = 0.6283185307 s,

or to three significant figures, 0.628 s.

For the 2.20 kg mass, 200.0 N/m spring system, the period is:

T = 2·π·√((2.20 kg)/(200.0 N/m)) = 0.6589860345 s,

or to three significant figures, 0.659 s.

Thus the 2.20 kg mass, 200.0 N/m spring system will have a longer oscillation period than the 0.100 kg mass, 10.0 N/m spring system.

Sections 70854, 70855
Exam code: quiz06Ho0k
(A) : 6 students
(B) : 38 students
(C) : 1 student
(D) : 0 students

Success level: 84%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.36