An unbalanced motor is mounted at the tip of a rigid beam of mass mb and length L. The bea...

An unbalanced motor is mounted at the tip of a rigid beam of mass mb and length L. The beam is restrained by a torsional spring of stiffness kt and an additional support of stiffness k located at the half length of the beam. In the static equilibrium position, the beam is horizontal and the torsional spring does not exert any moment on the beam. The mass of the motor is mm, and the unbalance results in a harmonic excitation F(t) = F sin ω0t in the vertical direction. Derive the equation of motion for the system assuming that θ is small.

Figure P9.39