Understanding the Spring-Mass System
The scenario involves a light spring and a ball, where the spring's potential energy is converted into kinetic energy as the ball moves. To calculate the maximum velocity of the ball, we need to analyze the system's energy transformations.

Key Parameters
- **Spring Length:** 20 cm
- **Force Constant (k):** 2 kg/cm

Potential Energy of the Spring
- The potential energy stored in a compressed or stretched spring is given by the formula:
**PE = (1/2) k x²**
where \( x \) is the displacement from the spring's natural length.

Finding the Maximum Compression/Extension
- In this case, if the spring is compressed, the maximum compression could be equal to its length (20 cm) when the ball is released.
- Convert the force constant into standard units:
**k = 2 kg/cm = 200 kg/m**

Calculating Potential Energy
- If the spring is compressed by its full length:
**PE = (1/2) * 200 N/m * (0.2 m)²**
**PE = (1/2) * 200 * 0.04 = 4 J**

Equating Potential Energy to Kinetic Energy
- At maximum velocity, all potential energy converts into kinetic energy (KE):
**KE = (1/2) m v²**
- Rearranging gives us:
**v = √(2 * PE / m)**

Finding Maximum Velocity
- Assuming the mass of the ball (m) is known, substitute the values into the equation to find the velocity. If m is not specified, the final answer will depend on that parameter.
This analysis shows that the maximum velocity of the ball occurs when the potential energy of the spring is fully converted into kinetic energy.