Differential Equations and The - Braun, Martin 7579 · Problem 2.12.Ex2

Introduction to Applied Nonlinear Dynamical Systems and Chaos — Braun, Martin 7579

Mathematics — Calculus · dirac-delta-impulse

Problem

Solve the initial-value problem

(d^2y/dt^2)+4(dy/dt)+5y=f(t)

;

y(0)=1

y'(0)=0

, where

f(t)

is an impulsive force which acts on the extremely short time interval

1\leq t\leq 1+\tau

, and

\int_1^{1+\tau}f(t)\,dt=2