ME3514_Impulse_Function_and_Impulse_Response_Part_1_2

# ME3514_Impulse_Function_and_Impulse_Response_Part_1_2 -...

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ME3514 Topics Transfer Function Block Diagram Transient Response Analysis using TF with MATLAB Unit Impulse (Delta) Function Impulse Delta function Momentum Relationship between momentum and impulse Laplace transform of an impulse Examples of impact problems R. Burdisso 1

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ME3514 Impulse What is an impulse? f(t) ) Units:[ . ] I ftd t Ns I = Area () U ts :[ .] t t What is the delta function δ (x)? A mathematical function ) 1 t d t t dt 1 It   R. Burdisso 2 t
ME3514 Impulse The delta function is used to model a force with short duration t) = Area () It f(t) I Area dt t t ft I t R. Burdisso 3

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ME3514 Impulse Relationship between I and momentum: What is momentum? v 2 momentum Units: Ns m mv Ns ms     To find relationship between I and momentum, let’s solve the following ynamic problem m dynamic problem 0 v 0 t 0 t f(t) F m i f v () f t t o t R. Burdisso 4
ME3514 Impulse EOM: 2 Fm a dx d v  tegrating EOM rt time 2 () f tm m dt dt Integrating EOM w.r.t. time t t o f td t mvt  (0 ) o Im v t v m v m v  Impulse = change in momentum f i R. Burdisso 5 NOTE: force time history f(t) is not important – only the impulse of the force

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ME3514 Impulse Example () f tI t I t dt t (0 ) 0 i vt  ) t ) ? f m It m 0 a t 0 ff f m Im v m m v v t I   R. Burdisso 6

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ME3514 Impulse Laplace Transform of the Delta function ) 1 () t   () 1 t dt Laplace of translated Delta function t   ts o tt e  o o t o t R. Burdisso 7
ME3514 Impulse

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ME3514_Impulse_Function_and_Impulse_Response_Part_1_2 -...

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