A body of mass m suspended from an ideal spring is executing simple harmonic oscillations. The force constant of the spring is k and the time period of the body is T. Show by dimensional method that the formula `T=2pim//k` is incorrect. Establish its correct form.

Explanation

To show that the formula \( T = \frac{2\pi m}{k} \) for the time period of a mass-spring system is incorrect and to establish its correct form, we will use the dimensional analysis method.

### Step 1: Write down the given formula
The formula we need to analyze is:
\[ T = \frac{2\pi m}{k} \]

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