{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw2_solution

# hw2_solution - Homework Set#2 MAE 4720/7720 – Modern...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework Set #2: MAE 4720/7720 – Modern Control, Fall 2008 Solution The governing equation for a simple mass-spring system is 4 = + z z a) the SSR is shown below: [ ] T z z = x - = 4 1 A Eigenvalues: ( 29 4 4 1 det det 2 = + = - =- λ λ λ λ A I Therefore, the eigenvalues are j 2 ± = λ (two purely imaginary numbers) The system (unforced) response is jt jt e K e K t z 2 2 2 1 ) (- + = = t a t a 2 cos 2 sin 2 1 + since t j t e jt 2 sin 2 cos 2 + = (Euler’s Theorem). So, we expect the unforced (natural) response to be a harmonic solution (sine/cosine functions) with no damping. b) STM using Laplace method: ( 29 [ ] + +- + + = - =- = Φ----- 4 4 4 4 1 4 4 1 ) ( 2 2 2 2 1 1 1 1 1 s s s s s s L s s L A sI L t Using Laplace tables: - = + +- + + = Φ- t t t t s s s s s s L t 2 cos 2 sin 2 2 sin 5 . 2 cos 4 4 4 4 1 4 ) ( 2 2 2 2 1 Note: if t = 0, the STM is a 2x2 identity matrix (as it should be) STM using diagonalization method: 1 ) (- = Φ P Pe t Dt The diagonalizing matrix is...
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

hw2_solution - Homework Set#2 MAE 4720/7720 – Modern...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online