Download presentation
Presentation is loading. Please wait.
1
1940 Tacoma Narrows Bridge Collapse
(see
2
Second-Order System Dynamic Response
The general expression for a 2nd-order system is This is a linear 2nd-order ODE, which can be rearranged as wn (= ) is the natural frequency, which equals for a RLC circuit and for a spring-mass-damper system. z is the damping ratio, which equals for a RLC circuit and for a spring-mass-damper system. ) a 2 / ( 1 =
3
Solutions to the ODE with Step-Input Forcing
For step-input forcing, there are 3 specific solutions of the ODE because there are 3 different roots of the characteristic equation (see Appendix I). =
4
The solution is of the form
where and with The two initial conditions used are and y(0)=0.
5
The solution is of the form
where and with OR with The two initial conditions used are and y(0)=0.
6
Underdamped Case (z < 1 )
The solution is Eqn. 5.57:
7
Critically Damped Case (z = 1 )
The solution is Eqn. 5.59:
8
Overdamped Case (z > 1 )
The solution is Eqn. 5.60:
9
Step-Input Forcing Terminology
wd ringing frequency Figure 5.7
10
Sinusoidal-Input Forcing
For sinusoidal-input forcing, the solution typically is recast into expressions for M(w) and f(w) (see Eqns and Appendix I). Figures 5.9 and 5.10
11
In-Class Example Consider the RLC circuit (R = 2 W; C = 0.5 F; L = 0.5 H).
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.