The maximum speed of an object oscillating with a given frequency and amplitude can be calculated using the formula:
Vmax = 2πfA
where: Vmax is the maximum speed, f is the frequency in hertz (Hz), and A is the amplitude in meters (m).
To use this formula, we need to convert the amplitude from millimeters (mm) to meters (m). Since 1 meter is equal to 1000 millimeters, we can convert the amplitude as follows:
Am = 90 mm = 90 / 1000 m = 0.09 m
Now we can substitute the values into the formula:
Vmax = 2π * 9 Hz * 0.09 m = 2π * 9 * 0.09 m/s = 2 * 3.14 * 9 * 0.09 m/s ≈ 5.07 m/s
Therefore, the maximum speed of the object oscillating at a frequency of 9 Hz and an amplitude of 90 mm is approximately 5.07 m/s.