lecture11

# lecture11 - Section 4.1 The Mass Spring Oscillator March 3...

This preview shows pages 1–5. Sign up to view the full content.

Section 4.1 The Mass Spring Oscillator March 3, 2009 The Mass Spring Oscillator

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

View Full Document
Today’s Session Section 4.1: A mechanical application of the general theory of second order DFQ’s There is a parallel (meaning same equation, but a di±erent interpretation) for electrical systems (which we will treat) A Summary of This Session: (1) Damped mass-spring oscillator; (2) Hooke’s law; (3) synchronization; (4) synchronous solution The Mass Spring Oscillator
Repeated Roots, 3rd order DFQ Example 1: (a) Solve y ′′′ + 3 y ′′ + 3 y + y = 0 (b) Show that y 2 = x y 1 , y 3 = x 2 y 1 are independent solutions to the problem in part (a). (c) Write down the general solution to the problem. Answer: The characteristic equation is: r 3 + 3 r 2 + 3 r + 1 = 0. This reduces to ( r + 1) 3 = 0. So r = 1 is a triple (repeated) root. The general solution looks like: y = C 1 e x + C 2 xe x + C 3 x 2 e x . The Mass Spring Oscillator

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

View Full Document
A second order DFQ with complex roots Example 2: (a) Solve y ′′ + 4 y = 0. (b) Solve
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 12

lecture11 - Section 4.1 The Mass Spring Oscillator March 3...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online