So in contrast to the discrete mass system, in distributed mass or continuous system the system has infinite number of natural frequencies and corresponding to each natural frequency, the system will have a distinct mode shape.
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It may be observed that the response of the continuous system depends time and space coordinate (location). But in case of discrete system the response is only a function of time. Hence while the equation of motion of discrete systems are written in terms of ordinary differential equations, in case of continuous system they are written in terms of partial differential equations.
- It may be noted that all the real systems are continuous system.
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A continuous system for analysis purpose can be reduced to a finite number of discrete models. Each discrete model can be reduced to an eigen value problem.
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In case of continuous system the solution yields infinite number of eigen values and eigen functions where as in discrete system the eigen values and eigen vectors are finite.
- The concept of orthogonality is applicable to both discrete and continuous systems.
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The eigen value problem in case of discrete system takes the from of algebraic equations while in continuous systems differential equations and some times integral equations are obtained. Eigenvectors of the discrete system becomes eigenfunction of the continuous system.