ABSTRACT
In many mechanical systems the motion is an oscillation with the position of static equilibrium as the center. Even a solid structure like a bridge or a concrete weir vibrates due to the action of wind, water, or earth tremors. With appropriate assumptions a mathematical model for such an oscillatory motion can be constructed. The chapter looks at a very simple situation which illustrates the essential features of an oscillatory motion. It shows that a system of linear differential equations can be written as a single differential equation of higher order. There are no hard and fast, rules whether to solve a problem as a system of first order differential equations or as a single higher order equation. A cubic polynomial has at least one real root, and since all the coefficients of the polynomial are positive, any real root must be negative to obtain zero on the right hand side of.
