To solve this problem, we can use the equation for the frequency of an oscillating mass-spring system:
f = 1 / T
where f is the frequency and T is the period.
Given that the frequency is 2.0 Hz, we can find the period:
T = 1 / f
T = 1 / 2.0 Hz
T = 0.5 s
The velocity of the mass, vx, at any point can be determined using the equation:
vx = -Aωsin(ωt + φ)
where A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase constant.
In this case, the mass is at x = 5.0 cm, so we can find the amplitude:
A = 5.0 cm = 0.05 m
The angular frequency can be calculated using the formula:
ω = 2πf
ω = 2π * 2.0 Hz
ω ≈ 12.57 rad/s
Now we can use the given velocity to find the phase constant:
vx = -Aωsin(ωt + φ)
-30 cm/s = -0.05 m * 12.57 rad/s * sin(12.57 rad/s * t + φ)
Since sin(12.57 rad/s * t + φ) = -1, we have:
-30 cm/s = -0.05 m * 12.57 rad/s * (-1)
-30 cm/s = 0.6285 m^2/s * m/s
-30 cm/s ≈ -0.63 m^2/s
To express the answer using two significant figures, we round the value to -0.63 m^2/s.
Therefore, the velocity of the mass is approximately -0.63 m^2/s.