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Unformatted text preview: 3 89Problems and Solutions Section 3.10 (3.65 through 3.71) 3.65*.Compute the response of the system in Figure 3.26 for the case that the damping is linear viscous and the spring is a nonlinear soft spring of the form k(x)=kx!k1x3and the system is subject to a excitation of the form (t1= 1.5 and t2= 1.6) F(t)=1500!(t"t1)" !(t"t2)[ ]Nand initial conditions of x= 0.01 m and v= 1.0 m/s. The system has a mass of 100 kg, a damping coefficient of 30 kg/s and a linear stiffness coefficient of 2000 N/m. The value of k1is taken to be 300 N/m3. Compute the solution and compare it to the linear solution (k1= 0). Which system has the largest magnitude? Compare your solution to that of Example 3.10.1. Solution: The solution in Mathcad is 3 90Note that for this load the load, which is more like an impulse, the linear and nonlinear responses are similar, whereas in Example 3.10.1 the applied load is a “wider” impulse and the linear and nonlinear responses differ quite a bit. 3.66*.Compute the response of the system in Figure 3.26 for the case that the damping is linear viscous and the spring is a nonlinear soft spring of the form k(x)=kx!k1x3and the system is subject to a excitation of the form (t1= 1.5 and t2= 1.6) F(t)=1500!(t"t1)" !(t"t2)[ ]Nand initial conditions of x= 0.01 m and v= 1.0 m/s. The system has a mass of 100 kg, a damping coefficient of 30 kg/s and a linear stiffness coefficient of 2000 N/m. The value damping coefficient of 30 kg/s and a linear stiffness coefficient of 2000 N/m....
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 Spring '09
 J.G.Lee
 Fundamental physics concepts, Linear system, initial conditions, Nonlinear system, linear stiffness coefficient

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