ADS Homework 7 - cos sin 1 1 1 1 = = The initial conditions...

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Homework 7: The system is an undamped system which is subjected to an impuls loading. The initial conditions are; 0 ) 0 ( ) 0 ( ; 0 ) 0 ( ) 0 ( = = = = = = v t v v t v There are two phases that must be examined for the system. Find the solution for the first phase. Solution: ) ( 0 t p kv v m = + : Equation of motion The two phases are: ) / ( ; ) ( : 0 ) 2 0 0 0 1 m k w p kv v m p t p t t a = = + = 0 ; 0 ) ( : ) 0 1 = + = kv v m t p t t b : 0 ) 1 t t a ) ( ) ( ) ( ) / ( 2 0 t v t v t v m k w p kv v m p c + = = = + t B t A t v c ϖ cos . sin . ) ( + = : Homogeneous Solution k p t v p 0 ) ( = : Particular Solution k p t B t A t v t v t v p c 0 cos . sin . ) ( ) ( ) ( + + = + = k p v B k p B t v 0 1 0 1 ) 0 ( ) 0 ( - = + = = 1

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ϖ ) 0 ( ) 0 ( sin . cos . ) ( 1 1 v A A t v t B t A t v = = = - = ( 29 t k p t v t v k p t k p v t v t v cos 1 cos ) 0 ( sin
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Unformatted text preview: . ) ( cos . ) ( sin . ) ( ) ( 1 1 1 1-+ + = + -+ = The initial conditions are given as; ) ( ) ( ; ) ( ) ( = = = = = = v t v v t v So the solution can be written as; ( 29 t k p t v cos 1 ) (-= 2...
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ADS Homework 7 - cos sin 1 1 1 1 = = The initial conditions...

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