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SolSec3.6 - 3 39 Problems and Solutions Section 3.6(3.37...

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3- 39 Problems and Solutions Section 3.6 (3.37 through 3.38) 3.37 A power line pole with a transformer is modeled by mx kx y ˙˙ ˙˙ + = − where x and y are as indicated in Figure 3.23. Calculate the response of the relative displacement ( x – y ) if the pole is subject to an earthquake base excitation of (assume the initial conditions are zero) ˙˙ y t A t t t t t t ( ) = > 1 0 2 0 2 0 0 0 m effective mass k effective stiffness x ( t ) y ( t ) Solution: Given: y kx x m & & & & = + ˙˙ ˙ y A t t t t t t x x = > ( ) = ( ) = 1 0 2 0 2 0 0 0 0 0 0 The response x ( t ) is given by Eq. (3.12) as x t F h t d t ( ) = ( ) ( ) 0 τ τ τ where h t m t n n ( ) = ( ) τ ω ω τ 1 sin for an undamped system For , 2 0 0 t t
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