In an aviation test lab, pilots are subjected to vertical oscillations on a shaking rig to see how well they can recognize objects in times of severe airplane vibration. The frequency can be varied from 0.0240 to 39.1 Hz and the amplitude can be set as high as 1.87 m for low frequencies.
A) What is the maximum velocity to which the pilot is subjected if the frequency is set at 20.9 Hz and the amplitude at 1.94 mm?
B) What is the maximum acceleration to which the pilot is subjected if the frequency is set at 20.9 Hz and the amplitude at 1.94 mm?
V(max)=a*2*pi*f=1.94*20.9*3.14*2=25.86cm/s
a(max)=v(max)*2*pi*f=3393cm/s^2
To determine the maximum velocity and acceleration to which the pilot is subjected, we'll need to use the formulas for simple harmonic motion.
A) Maximum Velocity:
The equation for maximum velocity (Vmax) of a mass undergoing simple harmonic motion is given by:
Vmax = 2πfA
where:
f is the frequency in Hz
A is the amplitude in meters
To find the maximum velocity, plug in the given values:
f = 20.9 Hz
A = 1.94 mm = 1.94 × 10^(-3) m
Vmax = 2π(20.9)(1.94 × 10^(-3))
Vmax ≈ 0.256 m/s
Therefore, the maximum velocity to which the pilot is subjected is approximately 0.256 m/s.
B) Maximum Acceleration:
The equation for maximum acceleration (amax) of a mass undergoing simple harmonic motion is given by:
amax = (2πf)^2 A
Using the same given values:
f = 20.9 Hz
A = 1.94 mm = 1.94 × 10^(-3) m
amax = (2π(20.9))^2 (1.94 × 10^(-3))
amax ≈ 4.58 m/s^2
Therefore, the maximum acceleration to which the pilot is subjected is approximately 4.58 m/s^2.