Final answer:
The maximum speed reached by the mass is 0.025π m/s. Hence, option (b) is correct.
Step-by-step explanation:
First, let's find the period of the oscillation using the formula T = 2π/ω, where T is the period and ω is the angular frequency. In this case, the period is given as π/2 seconds, so we can plug that into the formula to find ω:
T = 2π/ω ⟶ π/2 = 2π/σ ⟶ ∠/2 = σ ⟶ σ = π/2 radians/s
The maximum speed of the mass can be found using the formula v_max = Aω, where v_max is the maximum speed, A is the amplitude, and ω is the angular frequency.
The amplitude is given as 5 cm, which we can convert to meters (1 m = 100 cm) and then plug into the formula:
v_max = (5 cm)( π/2 radians/s) ⟶ [5 cm * (1 m/100 cm)]( π/2 radians/s) ⟶ 0.05 m * π/2 rad/s ⟶ 0.025π m/s
Therefore, the maximum speed reached by the mass is 0.025π m/s, which is option b.