Question

A cantilevered steel beam has an extensible wire of unknown material connected at its endpoint (see diagram). A weight of 250 N is seen hanging from the wire. When beam- wire-mass vibrates, it acts like a single degree of freedom system. Given the following parameters: Lwire 4 meters Awire-0.11 m2 Ewire=70 GPa Lbeam-6 m Ebeam 206 GPa Ibcam-0.25 m2 L EI a) Determine the equivalent spring constant for the system. b) Find the natural frequency of the system c) If the initial displacement of this system, xo, is 50 cm, what would be the maximum velocity that the system would attain if the initial velocity, Vo 0.2 m/sec? d) Suppose that a damper, c, were now added to the system at L/2, what would be the value of the damper if it were moved to the end of the beam so that the system would act m like a one-degree of freedom system? e) What would be the minimum value of the damping constant to produce aperiodic motion? Give the value in N-s/m f with the given values of vo and Xo, and the e value from part e), find the overshoot.

Answer 1

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