The motion y(t) is the input to the system and the motion of the body x(t) is the output of the system. A motorcycle is travelling at a speed of 55 mph on a road with a sinusoidal elevation. The distance between peak-to-trough is 3 ft and the distance between two consecutive peaks is 50 ft. The natural frequency of the suspension system is 5 rad/sec and the damping ratio is 0.2. Determine the amplitude of vibration in x.

Present the equations of motion of the attached two-degree-of-freedom system in the main coordinate system. Determine a value for α such that the equations of motion can be solved in the principal coordinate system. If it is assumed that the type of damping is Rayleigh damping (10% proportional to mass and the rest proportional to stiffness), then determine the relative damping coefficient and damping constants for the structure.

The following mass-and-spring system has stiffness matrix K. For the mks values, find the two natural frequencies of the system and describe its two natural modes of oscillation. k₁ k₂ K3 K= - (K₁ + K₂) k₂ m₁ = 1, m₂ = 5; k₁ = 3, k₂ = 15, k3 = 15 k₂ - (K₂ + K3) Describe the mode of oscillation for w₂. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The two masses move linearly, staying a fixed distance apart. B. The two masses oscillate in the same direction, where the amplitude of m₁ is O C. The two masses oscillate in opposite directions, where the amplitude of m₁ is D. The two masses oscillate in the same direction with equal amplitudes. E. The two masses oscillate in opposite directions with equal amplitudes. times the amplitude of m2. times the amplitude of m₂.

Obtain X1(s)/F(s) and then determine the damping coefficient C of the mechanical system below. m2 =160.1 kg, k =953.7 N/m, k, =1,451.7 N/m, b, =148.0 N-s/m. X1(t) x2(t) k2 f2(t) m2 k, b2 massless plate Sonraki