mass m equal to the mass of the roof shown and its lateral stiffness k is equal to the sum of the stiffnesses of where an overdot denotes differentiation with respect to time; thus u denotes the ve locity of the mass and u its acceleration. The solution of this equation, presented in
Chapter 2, will show that if the mass of the idealized systems of Fig. 1.1.3 is dis placed through some initial displacement u(O), then released and permitted to vibrate freely, the structure will oscillate or vibrate back and forth about its initial equilib rium position. As shown in Fig. 1.1.3c, the same maximum displacement occurs oscil-