Question

2. Consider the system shown in the figure below, comprised of the same motor, steel beam, steel cable and crate All assumptions and properties are the same with one exception; the cable is no longer considered as rigid Cable properties: length = 4 m, diameter = 0.007 m, E = 207 GPa, Calculate the equivalent stiffness of the cable, in units of N/m. (See table 4.1.1 in your textbook) Draw an equivalent system diagram where the beam and cable each look like typical springs and the motor and beam-equivalent-mass are lumped into one mass. Calculate the static deflection of the crate, in meters. Write the equation(S) of motion for the displacement of the motor/beam and the crate from their static equilibrium positions. The applied force F(t) is the system input. a) b) Ymotort) c) d) crate(t) F(t) 3. In the spring arrangement shown in the figure below, the displacement x (the output) is caused by the applied force f (the input) on the end of a rigid bar. The system is in static equilibrium when x = 0, and the bar is vertical. Suppose that when a force f is applied there is only a small displacement x. That means the angle of the rigid bar as measured from a vertical line through the pivot point, θ, is small 8, if θ is measured in radians. Hint: when angles are small, sinθ This means that: the linear displacement of the top of the bar is x = 66 the displacement of the top spring is 50 the displacement of the lower spring is 2θ Determine the equivalent spring constant Re such that HT 6

Answer 1

m2i2 p. E F2, F2 = Fr 11142 82 = 12 日, 1, maro 'm 2
8