An exhaust pipe is used for a newly developed gasoline engine in the laboratory. It was decided to support the pipe by identical supports shown in the FIG. 1 below. Assume the effect from the gas exhaustion can be modeled by a lateral concentrated load f(t) = F cos(wt) applied at the end of the pipe, where the parameters w is the engine's speed and Fo is proportional to the exit pressure of the engine. The exhaust pipe and its supports form a system that can be modeled by a 2DOF lump mass system (FIG. 2). For the lump mass model, the vibration of the pipe can be characterized by the displacement of the mass center of the pipe, x, and the orientation of the pipe, O. The support may be modeled as a linear spring of spring constant k = 45,000 N/m. The damping characteristic of the support is assumed to be of the viscous type and has an approximate damping coefficient range c < 50 kg/s. Assume the pipe is made of 304 Stainless Steel material with density p = 8 g/cm and Young's modulus E = 193 GPa. The pipe length is 1 = 0.9 m and the pipe mass m is approximately 7.6 kg. The testing condition corresponds to Fo = 5 and covers the forcing frequency range 650 ~1500 rpm. During the test, it was observed that the pipe was shaking with excess vibration at certain frequencies. Your objectives is to propose a vibration suppression strategy (isolator, absorber) so that the vibration amplitude at the mass center is limited to within 1 cm in the frequency range. 0.6 0.3 F(t) ro: 0.168 ri: 0.167 G- 0.15 FIG 1. Schematic of the exhaust pipe and the supporting bearings. All units are in meter. G- x FIG 2. The vibration of the pipe as a 2DOF lump mass system.