The vibrations of the body of a helicopter due to the periodic force applied by the rotation of the rotor can be modeled by a frictionless spiring-mass-da system subjected to an external periodic force. The position x(t) of the mass is given by the equation:
x(t) = 2f0/ ω2n €“ ω2 sin(ωn €“ ω/2 t) sin(ωn €“ ω/2 t)
where F(t) = F0sin ωt, and fo = F0/m, ω is the frequency of the applied force, and m11 is the natural frequency of the helicopter. When the value of m is close to the value of ωn, the vibration consists of fast oscillation with slowly changing amplitude called beat. Use Fo/m = 12N/kg, ωn €“ 10rad/s, and ω = 12 rad/s to plot x(t) as a function of t for

Transcribed Image Text:

FrO im