Final answer:
The mass attached to the spring in simple harmonic motion is approximately 0.445 kg, calculated using the formula for the period of a spring-mass system.
Step-by-step explanation:
To determine the unknown mass on the spring in a simple harmonic motion, we use the formula T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. Given that the spring completes 10 cycles in 3.50 seconds, the period (T) is 3.50 s / 10 = 0.35 s. The spring constant (k) is given as 225 N/m. Rearranging the formula to solve for mass (m), we get m = kT² / (4π²).
Plugging in the values, we have m = (225 N/m × (0.35 s)²) / (4π²) ≈ 0.445 kg. Therefore, the mass attached to the spring that results in a simple harmonic motion with the given period is approximately 0.445 kg.