The frequency of oscillation of a mass m suspended by a spring is `n _(1)` . If the length of the spring is cut to one-half, the same mass oscillates with frequency `n_(2).` Determine the value of `n _(2) // n _(1).`

Explanation

To solve the problem, we need to determine the ratio of the frequencies of oscillation of a mass suspended by a spring before and after the spring is cut in half. Let's break down the solution step by step.

### Step 1: Understand the relationship between frequency and spring constant
The frequency of oscillation \( n \) of a mass \( m \) suspended by a spring with spring constant \( k \) is given by the formula:
\[ n = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \]

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