Final answer:
The period of a 0.500-kg mass on a spring with the given velocity function is calculated using the relationship between period and angular frequency, which is T = 2π/ω, where ω is given in the velocity function.
Step-by-step explanation:
The student is asking about the period of oscillation for a 0.500-kg mass attached to a spring with a given velocity function.
To find the period of the mass-spring system, we can look at the velocity function vx(t) = (3.60 cm/s) sin[(4.71 s⁻¹)t - π/2]. The argument of the sine function, (4.71 s⁻¹)t - π/2, gives us the angular frequency ω, where ω is 4.71 s⁻¹. The period T can be found by using the relationship T = 2π/ω.
By calculating T = 2π/4.71 s⁻¹, we determine the period of the mass-spring system.