Transforms of Discontinuous and Periodic Functions

Author: John J Weber III, PhD Corresponding Textbook Sections:

Expected Educational Results

Transforms of Discontinuous and Periodic Functions

Solving IVPs with Discontinuous Inputs

Investigation 13

Solve the following:

  1. y(t)+2y(t)={(t1)21t<30elsewhere, y(0)=0, y(0)=1

  2. y(t)+2y(t)={00t<1t11t<21t2, y(0)=0

  3. y(t)+4y(t)=u(t1)cos(t), y(0)=1, y(0)=2

  4. 2y(t)+y(t)+2y(t)={15t200elsewhere, y(0)=0, y(0)=0

  5. y(t)+y(t)=10[u(tπ)u(t2π)], y(0)=, y(0)=1

  6. y(t)+y(t)=f(t), y(0)=0, y(0)=0, where f(t)=t on 0<t<2 with period 2.

  7. y(t)+2y+3y(t)=f(t), y(0)=0, y(0)=0, where f(t)=e2t on 0<t<1 with period 1.

CC BY-NC-SA 4.0

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

Last Modified: Sunday, 8 November 2020 22:02 EDT