An object (object #1) of mass M is attached to a spring with spring constant k.

Question

An object (object #1) 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 #2) 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 #1 compare to that of object #2?

The frequency of object#2 is lower than that of #1.

The frequency of object#2 is higher than that of #1.

The frequencies are the same.

Explanation / Answer

f1=sqrt(k/m)/2pi

f2=sqrt((k/2+k/2)/m)/2pi=sqrt(k/m)/2pi

The frequencies are the same.

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