Physics quiz question: mass-spring strength constant

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA

A 0.75 kg mass attached to a horizontal spring has a 2.0 s period of oscillation. Neglect friction and drag. The spring strength constant of this spring is:
(A) 7.6×10^–2 N/m.
(B) 5.6 N/m.
(C) 7.4 N/m.
(D) 9.9 N/m.

Correct answer (highlight to unhide): (C)

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

T = 2·π·√(m/k),

such that the spring strength constant k will be:

k = m·(2·π/T)² = (0.75 kg)·(2·π/(2.0 s))² = 7.4022033008... kg/s²,

or as expressed in more conventional units to two significant figures, the spring constant is 7.4 (kg·m/s²)·(1/m) = 7.4 N/m.

(Response (A) is m·(T/(2·π))²; response (B) is (m·2·π/T)²; and response (D) is m·2·π/T.)

Sections 70854, 70855
Exam code: quiz06POr7
(A) : 6 students
(B) : 5 students
(C) : 40 students
(D) : 1 student

Success level: 77%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.58