How Does Laplace Transform Solve the Harmonic Motion Differential Equation?

[Jim wah]

(2.) Let the differential equation ¨x + 2 ˙x + 2x = 6 sin(t)U(t − 3π/2) , x(0) = 2, x˙(0) = 2

Solve for the position function x(t) using the Laplace transform:

 

[BvU]

Hi Jim,

Use the template provided for such things. It helps you order your thoughts and you get much better assistance.:

Homework Statement

obvious​

Homework Equations

what can you mobilize to deal with this ? notes, textbook, ...​

The Attempt at a Solution

Solution of the homogeneous equation is ...
what does Laplace do with equations like this ?​

 

[HomogenousCow]

Solve for the position function x(t) using the Laplace transform: