Final answer:
The oscillation frequency of spring 2, which has a spring constant half that of spring 1, will be the frequency of spring 1 divided by the square root of 2, or f/√2.
Step-by-step explanation:
The student is asking about the relationship between spring constants and the frequency of oscillation in simple harmonic motion when the mass is the same for two springs with different spring constants. The oscillation frequency of a spring is given by the formula f = (1/2π) * √(k/m), where f is the frequency, k is the spring constant, and m is the mass attached to the spring. For spring 1, with a spring constant k and oscillation frequency f, the frequency of spring 2 with spring constant k/2 can be calculated as follows:
f1 = (1/2π) * √(k/m)
f2 = (1/2π) * √((k/2)/m)
Since spring 1 frequency is given by f, we have:
f1 = f
f2 = (1/2π) * √(1/2) * √(k/m)
f2 = f * √(1/2)
f2 = f / √2
Therefore, the oscillation frequency of spring 2 is f divided by the square root of 2, or f/√2.