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SolSec 4.6

# SolSec 4.6 - Problems and Solutions for Section 4.6(4.61...

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Problems and Solutions for Section 4.6 (4.61 through 4.67) 4.61 Calculate the response of the system of Figure 4.16 discussed in Example 4.6.1 if F 1 ( t ) = δ ( t ) and the initial conditions are set to zero. This might correspond to a two-degree-of-freedom model of a car hitting a bump. Solution: From example 4.6.1, with F 1 ( t ) = δ ( t ), the modal equations are ) ( 7071 . 4 4 . ) ( 7071 . 2 2 . 2 2 2 1 1 1 t r r r t r r r δ δ = + + = + + & & & & & & Also from the example, rad/s 9899 . 1 1 . rad/s 2 rad/s 4106 . 1 07071 . rad/s 2 d2 2 2 d1 1 1 = = = = = = ω ζ ω ω ζ ω n n The solution to an impulse is given by equations (3.7) and (3.8): t e m F t r di t di i i ni i ω ω ω ζ sin ˆ ) ( = This yields r ( ) . sin . . sin . . . t e t e t t t = 5013 1 4106 3553 1 9899 1 2 The solution in physical coordinates is x r x ( ) ( ) . . . . . sin . . sin . ( ) . sin . . sin . . sin . . sin . / . . . . . . t M P t e t e t t e t e t e t e t t t t t t = = = + 1 2 1 2 1 2 1 2 2357 2357 7071 7071 5013 1 4106 3553 1 9899 1182 1 4106 08374 1 9899 3544 1 4106 2512 1 9899 9899 t

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