An object (object A) of mass M is attached to a spring with spring constant k. The other end of the spring is attached to a rigid wall. A second object (object B) of mass M is attached to two springs (one on each side of the object), each with a spring constant of k/2 (the other ends of the springs are attached to rigid walls). Each object is displaced and let go, causing harmonic motion. How does the frequency of oscillation of object A compare to that of object B?
A)The frequencies are the same.
B)The frequency of object B is higher than that of A.
C)The frequency of object B is lower than that of A.

Question

Quizplus · Accepted Answer

The frequency of oscillation of an object attached to a spring is given by f = (1/2π)√(k/m), where k is the spring constant and m is the mass of the object. In this case, object A has a spring constant of k and a mass of M, so its frequency is fA = (1/2π)√(k/M). Object B has two springs, each with a spring constant of k/2, and a mass of M, so its frequency is fB = (1/2π)√((k/2)/M) = (1/2π)√(k/2M). Therefore, the frequency of oscillation of object B is higher than that of object A.

An Object (Object A) of Mass M Is Attached to a Spring