MT-1620 al.2002 This is known as Duhamel's integral or The convolution integral oI The linear superposition integral This is a general case. For the particular single spring-mass system q()「F()o(-r m oJo response to arbitrary F(t Additional initial conditions (velocity and displacement can be added to this through the homogeneous solution to give q(u tC F()sho(t-t)lr +U snot +L(o)cost Of all the arbitrary forces, there is one form of particular interest Paul A Lagace @2001 Unit 20-18MIT - 16.20 Fall, 2002 This is known as: Duhamel’s integral or The convolution integral or The linear superposition integral This is a general case. For the particular single spring-mass system: 1 t () = m ω ∫0 q t F() τ sin ω (t − τ ) dτ response to arbitrary F(t) Additional initial conditions (velocity and displacement) can be added to this through the homogeneous solution to give: 0 () = m 1 ω ∫0 t F() sin ω (t − τ ) dτ + q ˙( ) q t τ sinω t ω + q( ) 0 cosω t Of all the arbitrary forces, there is one form of particular interest: Paul A. Lagace © 2001 Unit 20 - 18