When a massless spring is hung vertically and a mass is suddenly attached to it, the system will undergo Simple Harmonic Motion (SHM) as long as the spring obeys Hooke's Law.
The period of oscillation for a mass-spring system can be calculated using the formula:
T = 2π√(m/k)
where T is the period of oscillation, m is the mass attached to the spring, and k is the spring constant.
However, in this case, the given spring is massless. A massless spring would have an infinite spring constant (k), which means that the period of oscillation would be extremely small, approaching zero. In practice, the system would oscillate at an extremely high frequency, making it difficult to observe.
In reality, most springs have some mass and a finite spring constant, so the period of oscillation is non-zero and observable. But if we consider an ideal massless spring, the period of oscillation would technically be zero.
It's important to note that a true massless spring does not exist in the physical world, as all springs have some mass. The concept of a massless spring is often used in idealized physics scenarios to simplify calculations or illustrate theoretical concepts.