Barron's 2nd Edition DT Q56

Barron's Book

56) This problem asks us to consider the relation between mass and the frequency of oscillation. We can start by looking at the period(T) of an oscillating spring system.

Where T is the oscillation period, m is the hanging mass, and k is the spring constant

We need the frequency(f) of the oscillation, which can be found by taking the reciprocal of the period.

Where T is the oscillation period, m is the hanging mass, and k is the spring constant

If we assume our spring constant as "k", the above equation will represent our frequency with a mass of m. Now, if the mass were to be replaced with one of 2m, the frequency would be affected as shown below.

Where T is the oscillation period, m is the hanging mass, and k is the spring constant

When we replace m with 2m we are dividing the right side by root(2). In order to balance the equation, we need to divide the left side by root(2) as well.

Answer: B