Final answer:
The student's question pertains to calculating the time period of oscillation for a mass hanging from a spring attached to a metallic wire. If the wire's elasticity is not considered, the time period T can be found using the formula T = 2π√(m/k), where m is the mass and k is the spring constant. The elasticity of the wire complicates the calculation and would require additional information.
Step-by-step explanation:
The question deals with a mass m hanging from a massless spring with spring constant k, attached to a long metallic wire. The entire setup acts as a system capable of undergoing simple harmonic motion (SHM). The time period T of oscillation for such a system can be determined using the physics of simple harmonic motion. Specifically, when a body oscillates with SHM, the period of oscillation is given by the formula T = 2π√(m/k), where m is the mass of the oscillating object and k is the spring constant.
However, the provided information includes a metallic wire with a Young's modulus y, length l, and area of cross-section a. These factors can affect the effective spring constant of the system if the wire's elasticity is taken into account. To find the effective spring constant for the combined system of wire and spring, one must account for the wire's potential to stretch under the influence of the mass m, which is a more complex problem requiring additional information not provided in the question.
Assuming the wire does not significantly affect the spring constant, and using the spring constant k and mass m given, the time period T for the mass oscillating on the spring (ignoring any contribution from the wire's elasticity) would be calculated with the mentioned formula T = 2π√(m/k).