The frequency of oscillation of a vertical spring is $f$ when the mass hanging from the spring is $m$ - AQA - A-Level Physics - Question 31 - 2019 - Paper 1

To find the relationship between the frequency of oscillation $f$ and the mass $m$ hanging from the spring, we can use the formula for the frequency of a mass-spring system given by:

f = rac{1}{2\pi} \sqrt{\frac{k}{m}}

where $k$ is the spring constant. From this equation, we can see that:

1. The frequency is inversely proportional to the square root of the mass:

   $f \propto \frac{1}{\sqrt{m}}$

Hence, as the mass increases, the frequency of oscillation decreases. Therefore, the correct answer is:

A: $f \propto m^{-\frac{1}{2}}$.