MT-1620 al.2002 Figure 20.8 Representation of arbitrary force with time as series of impulses F over any interval aτ 叫k-△℃ Impulse=F(18t-I The response to any particular impulse is q(t)=vF(τ)τh(t-) where h(t-t)is characteristic response of system to an impulse So the total response is the summation of the responses to all the impulses In the limit, there are infinite impulses leading to the integral q(EO F(G)t-1)4r Paul A Lagace @2001 Unit 20-17MIT - 16.20 Fall, 2002 Figure 20.8 Representation of arbitrary force with time as series of impulses over any interval ∆τ: Impulse = F (τ) δ (t - τ) The response to any particular impulse is: q t( ) = F (τ ) ∆τ h(t − τ ) where h(t - τ) is characteristic response of system to an impulse. So the total response is the summation of the responses to all the impulses. In the limit, there are infinite impulses leading to the integral: t q t() = τ ∫0 F() h(t − τ ) dτ Paul A. Lagace © 2001 Unit 20 - 17