
10 Nonlinear and Stochastic Dynamic Models
Section 10.0.2: Examples of Nonlinear Vibration
10.1. Figure 10.1 compares sin θ versus θ, showing the effect of the nonlinearity as θ increases. Find the
values of θ for which the error is 5%, 10%, and 15%. The percent error can be defined as
% error =
θ −sin θ
sin θ
×100%.
Solution: The percent error equation can be rearranged to be a function of θ such that we can solve for it
given a particular error.
Let err be the percent error, then
100
θ −sin θ
sin θ
= err.
The figure below shows θ vs. % error, where we can estimate the values of θ for which the error is 5%, 10%,
and 15%.
Percent error as a function of θ.
The