The periodic time of a mass suspended by a spring (force constant K) is T. If the spring is cut in three equal pieces, what will be the force constant of each part? If the same mass be suspended from one piece, what will be the periodic time?

Explanation

To solve the problem step by step, we will first determine the force constant of each part of the spring after it is cut into three equal pieces, and then we will calculate the new periodic time when the mass is suspended from one of these pieces.

### Step 1: Understand the relationship between force constant and periodic time
The periodic time \( T \) of a mass \( m \) suspended from a spring with force constant \( K \) is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{K}} \]

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