MT-1620 a.2002 To get the result, integrate the equation over the regime where the force s nonzero (t=τtoτ+e) T+E T+E mi. dt+k q dt ∫ 8(t-r)dt use trapezoidal rule Trapezoidal rule q=5[q(B)+q(4)]x(B-t) This gives de de m +ka(t+e)+q( dt d T+E 0“ goes to zero 0 from Initial from since 8→>0 Condition Initial Condition al this results in Paul A. Lagace @2001 Unit 20-12  MIT - 16.20 Fall, 2002 To get the result, integrate the equation over the regime where the force is nonzero (t = τ to τ + ε) 2 + τ ε + τ ε + ⇒ ∫ττ ε m dq dt + k ∫τ q dt = ∫τ δ (t − τ ) dt dt 2 use trapezoidal rule Trapezoidal Rule: B 1 ∫A q dt = 2 [q (B) + q (A)] × (tB − tA ) This gives: ⇒ m  dq  −  dq   + k 1 [q (τ + ε) + q ( ) τ ]ε = 1  dt  τ ε  dt  τ  2 + = 0 goes to zero = 0 from Initial from since ε→0 Condition Initial Condition All this results in: Paul A. Lagace © 2001 Unit 20 - 12