5. (15 points) As shown in Figure 4, A homogenous rod with a fixed left end and a spring connected to the right end. Rod

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5 15 Points As Shown In Figure 4 A Homogenous Rod With A Fixed Left End And A Spring Connected To The Right End Rod 1 (262.53 KiB) Viewed 32 times

5. (15 points) As shown in Figure 4, A homogenous rod with a fixed left end and a spring connected to the right end. Rod parameters: the length is 1, cross section area is A, material density is p, elastic modulus is E. and the stiffness of the spring is k, Where E, A, p and m are units 1, and 1 = 26. (1)Try to derive the differential equation of longitudinal motion and give the boundary conditions; (2)Try to derive the frequency equation of the system, when the stiffness k=0; (3)Try to gain the natural frequency and modal function respectively, when the stiffness k=∞o. 1 Fig.4