A forcing F (t)=fosint acts at the end of the thin, homogeneous bar of the two-DOF...

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A forcing F (t)=fosint acts at the end of the thin, homogeneous bar of the two-DOF system shown below. The wheel can be modeled as a cylinder with mass m, radius R and rolls without slipping. The response of the system is to be described by the coordinates x(t) and 6 (t). Let g /L = 2k /m. 0 m, R m, L F(t) 9 a) Derive the particular solutions xp (t) and Op (t) for the system. b) At what values of the temporal frequency 2 does resonance occur in the system? c) Show that the "shape" of the response is that of the first mode when excited at the first natural frequency, and that the shape is that of the second mode when excited at the second natural frequency.- d) At what values (if any) of the temporal frequency 2 do anti-resonances occur for xp (t)? For Op (t)? e) Make plots for the amplitudes of xp (t) and Op (t) vs. the temporal frequency 2. A forcing F (t)=fosint acts at the end of the thin, homogeneous bar of the two-DOF system shown below. The wheel can be modeled as a cylinder with mass m, radius R and rolls without slipping. The response of the system is to be described by the coordinates x(t) and 6 (t). Let g /L = 2k /m. 0 m, R m, L F(t) 9 a) Derive the particular solutions xp (t) and Op (t) for the system. b) At what values of the temporal frequency 2 does resonance occur in the system? c) Show that the "shape" of the response is that of the first mode when excited at the first natural frequency, and that the shape is that of the second mode when excited at the second natural frequency.- d) At what values (if any) of the temporal frequency 2 do anti-resonances occur for xp (t)? For Op (t)? e) Make plots for the amplitudes of xp (t) and Op (t) vs. the temporal frequency 2.

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Step1 To derive the particular solutions for the system we need to solve the equations of motion The equation of motion for the translational motion i... View the full answer