Final answer:
The mass of the block attached to the spring is found to be approximately 0.149 kg or 149 grams, calculated using the formula relating frequency, mass, and spring constant.
Step-by-step explanation:
The student has asked to find the mass of a block oscillating on a spring with a frequency of 4.0 Hz and a known spring constant of 75 N/m. The relationship between the mass (m), spring constant (k), and frequency (f) of a simple harmonic oscillator is given by the formula f = 1/(2π)∙√k/m. Solving for the mass yields m = k/(4π²f²).
In this case, the frequency (f) is 4.0 Hz and the spring constant (k) is 75 N/m:
m = 75 N/m / (4π² × (4.0 Hz)²) = 75 / (16π²) = 0.149 kg
Therefore, the mass of the block is approximately 0.149 kg or 149 grams.