## Assignment-Single degree of freedom system

Learning objective:
Upon the completion of this chapter student will be able to:
 Develop a clear idea regarding the idealized dynamic system
 Solve damped and undamped single degree of freedom (SDOF) system
 Familiar with the responses of SDOF system under different types of force and impulse
 Understand how stiffness should be combined with each other in series or parallel
connection
 get an very basic insight of SDOF system response at the time of earthquake
3.1. Idealization of Dynamic system
Dynamic analysis requires a huge computational effort. That is why, dynamic system
idealization is very important. Response of every portion of a system is not always required, so it
is a common practice to reduce the structure to a simple dynamic model for analysis. For
example, a bridge is usually represented as a spring and a mass system for analysis, although
there is no as such similarity between the spring mass model and the bridge. Similarly, the stories
of multistoried building are represented as lumped mass at floor levels and column as equivalent
springs. Actually, an accurate idealized model should represent the required behavior or
phenomenon of the system. Figure 3.1 represents spring and mass models of SDOF system of
water-tank.

The basic need of the idealization is to reduce the degree of freedom of a system for evaluation
of response. Degree of freedom means, the number of independent direction where a body can
move. The direction must be independent to each other. In simple words there should not be any
component of the one direction to other directions. The spring mass system can be develop by
first lumping the mass appropriately at location of mass concentration. For example, the mass of
a bridge is mainly concentrated at the deck and therefore the mass of the bridge should be
lumped at the deck level. In multistory building, stories are the main source of mass andthe
masses should be therefore be lumped at floor level. So, bridges, water tanks are generally
idealized as single degree of freedom system and similarly multistory buildings, continuous
structures like dams, silos, and chimneys are represented as multi-degree of freedom systems.
Degree of freedom: are the possible numbers of independent parameters that define its
configuration. But the combined response of a mass is calculated by adding the response of
single degree of freedom. The total response is the resultant of x, y and z axis’s response. The
response is calculated separately and then combined to get the resultant response.