Frequency natural undamped

Equations (3.42) and (3.43) are the standard forms of transfer functions for a second-order system, where K = steady-state gain constant, Wn = undamped natural frequency (rad/s) and ( = damping ratio. The meaning of the parameters Wn and ( are explained in sections 3.6.4 and 3.6.3. 

Consider a second-order system whose steady-state gain is K, undamped natural frequency is Wn and whose damping ratio is (, where C < 1 For a unit step input, the block diagram is as shown in Figure 3.18. From Figure 3.18... 

Equation (3.71) can only be used if the damping is light and there is more than one overshoot. Equation (3.67) can now be employed to calculate the undamped natural frequency... 

Thus, for a settling time of 0.1 seconds for a system that is critically damped, the undamped natural frequency is... 

For damped forced vibrations, three different frequencies have to be distinguished the undamped natural frequency, = y KgJM the damped natural frequency, q = /KgJM — cgJ2M) and the frequency of maximum forced amplitude, sometimes referred to as the resonant frequency. 

Oy variation of parameter j undamped natural frequency of tranfer function relating the variance of output i to nominally constant parameter, j... 

The cascade design procedure begins with a transfer function in factored form such as is shown in Eq. (7.156) and realizes the transfer function as a product of second-order transfer functions and, if the order is odd, a first-order transfer function. These constituent transfer functions are termed sections. For the transfer function in Eq. (7.156), we have three sections so that T = T TiT where Ti = l/(s -F 1), and Ti and T3 have the form l/(s + s ([Pg.644]

Many other filter sections that employ only one op-amp have been used over the years. Particular mention should be made of the Sallen-Key circuits (Budak, 1974) and J.J. Friend s single-amplifier-biquad(SAB) (Ghausi and Laker, 1981).The Friend SAB can realize second-order notch sections in which the undamped natural frequency of the zeros can differ from that of the poles. This is a feature that is needed if a higher-order bandstop filter is to be realized by cascading second-order notch sections. 

Takewaki Method The aim ofthe Takewaki (1997) method is to minimise an objective function given by the sum of the amplitudes ofthe interstory drifts ofthe transfer function, evaluated atthe undamped natural frequency of the structure, subject to a constraint on the total amount of added viscous damping. Initially the added damping is uniformly distributed and the optimum distribution is then achieved using a gradient-based search algorithm, that is, the damping distribution... 

Plots of the step responses for different values of i are shown in Figs. 5.8 and 5.9, where the time axis is normalized with respect to t. Thus, when t is small, a rapid response is signified, implying a large value for the undamped natural frequency, o) = 1/t. 

The cyclic radian frequency can also be related to the undamped natural frequency... 

Figure 7.17a shows the variation of the three undamped natural frequencies of the 3-DOF model with constant coefficient of friction as a function of lead screw... 

---