It may be noted from the 3rd term in Eq. (2.1.27) that the coefficient of the response θ is a time varying parameter. Hence this type of system is known as parametrically excited system and this equation is known as Mathieu-Hill type of equation. Taking cubic order nonlinear term, (2.12.6) will become the equation of a parametrically excited system with cubic nonlinearities.
..............................................................................................(2.1.28)
Exercise Problems
Problem 2.1.1 Derive the equation motion of a compound pendulum.
Problem 2.1.2 Derive the equation of motion a tuned vibration absorber considering the primary spring force equal to 
Problem 2.1.3 Derive the equation motion of the following system. Consider the spring to be a nonlinear spring having the spring force 
. Assume other elements to be linear.
Figure 2.1.6 System for exercise problem 2.1.3.