Final answer:
The maximum velocity of a simple harmonic oscillator can be determined using the equation v_max = Aω, where v_max is the maximum velocity, A is the amplitude of the oscillation, and ω is the angular frequency. The angular frequency can be determined using the equation ω = sqrt(k/m), where k is the spring constant and m is the mass of the system. Substituting the values into the equations, the maximum velocity is found to be approximately 54.23 m/s.
Step-by-step explanation:
The maximum velocity of a simple harmonic oscillator can be determined using the equation:
vmax = Aω
Where vmax is the maximum velocity, A is the amplitude of the oscillation, and ω is the angular frequency.
The angular frequency can be determined using the equation:
ω = sqrt(k/m)
Where k is the spring constant and m is the mass of the system.
In this case, the spring constant is 200 N/mm, which is equivalent to 200,000 N/m, and the mass is 6 kg. Therefore,
ω = sqrt(200,000/6)
ω ≈ 271.16 rad/s
Substituting the values of A and ω into the equation for maximum velocity:
vmax = (0.200 m)(271.16 rad/s) ≈ 54.23 m/s