SolSec3.10

# SolSec3.10 - 3 70 Problems and Solutions Section 3.10(3.58...

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3- 70 Problems and Solutions Section 3.10 (3.58 through 3.64) 3.58*. Compute the response of the system in Figure 3.22 for the case that the damping is linear viscous and the spring is a nonlinear soft spring of the form kx k x kx () =− 1 3 and the system is subject to a excitation of the form ( t 1 = 1.5 and t 2 = 5) F t tt ( ) ( ) [] 1500 12 ΦΦ N and initial conditions of x 0 = 0.01 m and v 0 = 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 k 1 is taken to be 300 N/m 3 . Compute the solution and compare it to the linear solution ( k 1 = 0). Which system has the largest magnitude? Compare your solution to that of Example 3.10.1. Solution: The solution in Mathcad is

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3- 71 3.59*. Compute the response of the system in Figure 3.22 for the case that the damping is linear viscous and the spring is a nonlinear soft spring of the form kx k x kx () =− 1 3 and the system is subject to a excitation of the form ( t 1 = 1.5 and t 2 = 1.6) F t tt ( ) ( ) [] 1500 12 ΦΦ N and initial conditions of x 0 = 0.01 m and v 0 = 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 k 1 is taken to be 300 N/m 3 . Compute the solution and compare it to the linear solution ( k 1 = 0). How different are the linear and nonlinear responses?
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• Spring '09
• abduljaba
• Fundamental physics concepts, Linear system, initial conditions, Nonlinear system, linear stiffness coefficient

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SolSec3.10 - 3 70 Problems and Solutions Section 3.10(3.58...

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