ENTC 395

1. ENTC 395 Lecture 5b 2nd Order Forced Response R. Bolton

2. Today • 2nd order ODEs with non-zero RH Sides • 2nd order ODEs with multi-term RH Sides • Complete solution

3. 2nd Order ODE Non-Zero RHS A complete solution of the ODE is the sum of the complementary solution and a particular solution. The complementary solution holds the transient response and the particular solution holds the steady-state response

4. Procedure for solution of 2nd order ODE with Non-zero RHS Method of undetermined coefficients 1. Solve for complementary solution 2. Select form of the particular solution from RHS and terms in complementary solution 3. Insert particular solution into ODE and solve for constants in particular solution 4. Solve for constants in the complementary part of the total solution using initial conditions

5. Complementary Solutions Start with one of the solutions below. Save the constants A&B for the initial conditions.

6. Particular Solutions The particular solution form is derived from the form of the RHS and complementary solution.

7. An Example

8. An exponential example

9. A harmonic example

10. A harmonic example